99 Commits
v1 ... master

Author SHA1 Message Date
d4a52a82a2 Change NonConcaveTC paper to accepted. 2025-12-01 09:53:08 +08:00
354a568787 Added paper with Lingfei and Qianyu; unbold submitted status. 2025-10-24 18:03:31 +08:00
74f2d3aed1 Added JOTA. 2025-10-02 09:40:05 +08:00
7f2560504b Added XYZ conference. 2025-10-02 09:35:12 +08:00
7c6f5fd135 Added Journal of the Operational Research Society to reviewer list. 2025-09-28 19:26:58 +08:00
3c9e5a2306 Added JQFA review. 2025-09-26 09:32:03 +08:00
4a9743236b Included updated time to LOB and perp. 2025-09-11 09:27:49 +08:00
d963a7fadf Correct capitalization. 2025-09-04 21:23:30 +08:00
1d5c46364a Updated font of acceptance. 2025-09-04 21:16:20 +08:00
1a64970923 Updated TaxTC to accepted. 2025-09-04 21:14:04 +08:00
732e25ae40 Added SIAM FM25. 2025-08-11 19:09:04 +08:00
a14581b383 Updated the date of perp paper. 2025-08-11 15:33:53 +08:00
3b66629287 Removed one paper. 2025-08-01 09:57:41 +08:00
3e272804f3 Change position. 2025-08-01 07:26:23 +08:00
f197f11468 Added arXiv link to arbitrage paper. 2025-07-15 10:12:06 -04:00
299476845c Fixed DEX arbitrage paper title. 2025-07-13 09:20:08 +08:00
21b4e93917 Updated DEX arbitrage SSRN link and LOB abstract. 2025-07-11 15:39:12 +08:00
039289cbd8 Roll back the paper link font to Georgia. 2025-06-30 15:35:46 +08:00
1da079b430 Remove italic from abstract. 2025-06-29 09:07:10 +08:00
71130358d0 Try American Typewritter 2025-06-29 09:01:29 +08:00
8d5af3ce57 Added variety of fonts. 2025-06-29 09:00:08 +08:00
f6b9bc2921 Add navbar blurred background. 2025-06-28 22:23:11 +08:00
24e12371ad Remember scroll position when refreshing. 2025-06-28 21:54:38 +08:00
ca22d5cd2a Fixed anchor jump location. 2025-06-28 21:51:02 +08:00
c73823b61d Adjusted the alignment of teaching block. 2025-06-23 13:15:31 +08:00
0b82c4cf85 Changed to Georgia for clarity on screen. 2025-06-23 10:07:39 +08:00
56daa0fdea Added fade-in effect for abstract. 2025-06-23 07:30:11 +08:00
eb2b826282 Added printer css. 2025-06-21 22:54:10 +08:00
c0002ca721 Adjusted contact block size. 2025-06-21 21:46:45 +08:00
8cd2b3afbb Simplified contract block style. 2025-06-21 21:42:28 +08:00
05b9c9f4bc Updated dynamic toggle icon. 2025-06-21 19:15:59 +08:00
318af764eb Add dynamic toggle icon 2025-06-21 19:02:44 +08:00
afd265cdcb Change toggle to icon. 2025-06-21 18:41:55 +08:00
f06d694fbd Remove comments. 2025-06-21 18:23:20 +08:00
6182d6d439 Cleaned up comments. 2025-06-21 18:03:33 +08:00
b762ae5f26 Added dark mode. 2025-06-21 18:01:13 +08:00
bedc40ad39 Added link for Yang Zhou. 2025-06-21 16:29:17 +08:00
7146b927f9 Added links for Zhou Yutian and Li Linfeng. 2025-06-21 16:09:05 +08:00
be4dd2d5c6 Removed underlines in author and paper links. 2025-06-21 14:34:08 +08:00
3f0e7c92a7 Updated boldness of link. 2025-06-21 14:09:40 +08:00
1bf2fb2ba7 Adjusted navbar size on mobile. 2025-06-21 14:08:36 +08:00
06a39c90d8 Change publication to numbered list. 2025-06-21 13:57:30 +08:00
2fa346acc1 Updated colorscheme to gruvbox light. 2025-06-21 13:52:12 +08:00
0c4702f3c1 Final choice: fixed scaling for table and auto scaling for the remainder. 2025-06-21 13:16:15 +08:00
c64ac3e575 Testing mobile table text size. 2025-06-21 13:05:29 +08:00
9433c3e635 Testing mobile table text size. 2025-06-21 13:04:08 +08:00
cce633aeaf Temporarily switched on mobile scaling. 2025-06-21 12:57:56 +08:00
0481bafc39 Change px to em 2025-06-21 12:55:03 +08:00
296daa9683 Changed several px to em. 2025-06-20 14:33:01 +08:00
5e7a17e90d Revert viewport change 2025-06-20 09:50:17 +08:00
44a6d52f70 Try alternative meta viewport setting. 2025-06-20 09:46:03 +08:00
2cc1d36abc Test mobile font scaling options. 2025-06-20 09:43:31 +08:00
556487ccc3 Fixed SEEM5410 course code. 2025-06-20 09:42:39 +08:00
32842b046f Reformat the css code. 2025-06-20 09:29:51 +08:00
a726119d13 Reformat the html code. 2025-06-20 09:29:09 +08:00
61e378f069 Revert "Updated notATable to description list."
This reverts commit 6362a6d82d.
2025-06-18 21:34:36 +08:00
6362a6d82d Updated notATable to description list. 2025-06-18 21:14:57 +08:00
835bfcfc0f Fixed the abstract link to the periodic paper. 2025-06-18 20:31:54 +08:00
53f7041b31 Added the periodic evaluation paper. 2025-06-18 17:35:58 +08:00
3e6e031a79 Added arxiv link to data asset paper. 2025-05-23 09:19:44 +08:00
b078b1b3db Fixed year in course list. 2025-05-21 22:52:36 +08:00
f9fac5f994 Simplify course list. 2025-05-21 22:50:52 +08:00
6a739f6ac7 Added link to data asset paper. 2025-05-21 22:37:08 +08:00
2acedc87c0 Updated two paper status to submitted. 2025-05-21 16:51:51 +08:00
ef8c68f163 Updated perpetual paper link. 2025-05-21 15:05:17 +08:00
c298771d13 Removed previous title of AMM paper. 2025-05-21 14:47:50 +08:00
12869f802f Added the data asset paper. 2025-05-21 14:04:31 +08:00
5afa984dc6 Added the perpetual paper. 2025-05-21 13:47:14 +08:00
202f9b8ae2 Fixed research interest table format. 2025-04-29 15:19:02 +08:00
7df09c2f41 Updated research interests, add stablecoins. 2025-04-29 15:09:48 +08:00
7f8a99dc4f Updated research interests for subcategories. 2025-04-29 15:08:04 +08:00
721edf3dfe Updated banner. 2025-04-29 14:45:07 +08:00
3adb0eab01 Updated research interests. 2025-04-29 14:39:50 +08:00
42e913e5d2 Added DEX arbitrage paper. 2025-04-25 09:52:28 +08:00
c920d24a26 Added time varying tax paper. 2025-04-22 07:19:41 +08:00
b84e663a0a Updated Stablecoin publication info. 2025-01-17 09:19:19 +08:00
d27fb8cee3 Updated the abstract of the tax+TC paper. 2024-12-31 18:24:02 +08:00
ce9998f036 Typo fix. 2024-11-26 08:58:29 +08:00
00ac83323d Updated the abstract of AMM paper. 2024-11-12 15:42:03 +08:00
9d460c5bd6 Updated AMM paper version. 2024-11-12 14:48:34 +08:00
0b226b016d Added INFORMS 2024. 2024-10-17 16:31:32 +08:00
8efe7e9b36 Fixed hythen in paper title. 2024-09-16 10:13:49 +08:00
bed6429673 Updated research interests. 2024-09-16 10:12:04 +08:00
e684acff65 Added links for coauthors. 2024-09-11 11:38:10 +08:00
ff2e75b700 Added TaxTC paper. 2024-09-11 11:36:35 +08:00
a05d0ba151 Updated courses for 2024-25. 2024-09-02 15:06:16 +08:00
67c03e0e2e Added stablecoin article link. 2024-08-30 11:06:44 +08:00
97322b9b23 Removed INFORMS HK announcement. 2024-08-26 14:49:57 +08:00
4a9d0af7cb Update Stablecoin paper title. 2024-07-29 10:40:37 +08:00
56c3ac94d0 Updated the Stablecoin paper. 2024-07-26 16:22:38 +08:00
2d011a7ef1 Update ICFE status. 2024-07-03 14:04:52 +08:00
d5ebd02b86 Added arXiv link of AMM paper. 2024-04-23 10:34:28 +08:00
741ec18da3 Updated research interests 2024-04-23 10:03:03 +08:00
4bf75b15d7 Addd page bottom animation. 2024-04-20 21:37:38 +08:00
e820c3a95f Fixed local abstract link. 2024-04-20 17:45:07 +08:00
04af56dfe4 Added localvol paper. 2024-04-20 17:42:23 +08:00
70a843c556 Added AMM paper. 2024-04-20 15:58:44 +08:00
9b9be14441 Removed DF submission. 2024-04-20 15:55:18 +08:00
c77bbad1d3 Updated conference, publications, and fixed links. 2024-02-09 13:19:26 +08:00
3 changed files with 1221 additions and 250 deletions

678
index.html Executable file → Normal file
View File

@@ -1,191 +1,557 @@
<!doctype html>
<html>
<head>
<head>
<link rel="stylesheet" href="style.css">
<link rel="stylesheet" media="print" href="style-print.css" />
<link rel="stylesheet" href="fontawesome-free-5.15.3-web/css/all.css">
<meta http-equiv="content-type" content="text/html; charset=utf-8">
<title>YANG, Chen</title>
<title>Homepage of YANG Chen @ SEEM, CUHK</title>
<script>
function toggleAbstract(absId) {
var x = document.getElementById(absId);
if (x.style.display === "none") {
x.style.display = "block";
} else {
x.style.display = "none";
var x = document.getElementById(absId);
if (x.style.display === "none") {
x.style.display = "block";
} else {
x.style.display = "none";
}
}
}
function toggleDarkLight() {
var element = document.body;
element.classList.toggle("dark_mode_body");
var elements = document.getElementsByClassName("authorlink")
for (const element of elements)
element.classList.toggle("dark_mode_authorlink");
var elements = document.getElementsByClassName("paperlink")
for (const element of elements)
element.classList.toggle("dark_mode_paperlink");
var elements = document.getElementsByClassName("extlink")
for (const element of elements)
element.classList.toggle("dark_mode_extlink");
var elements = document.getElementsByClassName("jourlink")
for (const element of elements)
element.classList.toggle("dark_mode_jourlink");
var elements = document.getElementsByClassName("ball");
for (const element of elements)
element.classList.toggle("dark_mode_ball");
var elements = document.getElementsByClassName("style-zero");
for (const element of elements)
element.classList.toggle("dark_mode_style-zero");
var elements = document.getElementsByClassName("style-one");
for (const element of elements)
element.classList.toggle("dark_mode_style-one");
var icon = document.getElementById("toggleICON");
icon.classList.toggle("fa-sun");
}
document.addEventListener("DOMContentLoaded", function (event) {
var scrollpos = sessionStorage.getItem('scrollpos');
if (scrollpos) {
window.scrollTo(0, scrollpos);
sessionStorage.removeItem('scrollpos');
}
});
window.addEventListener("beforeunload", function (e) {
sessionStorage.setItem('scrollpos', window.scrollY);
});
</script>
</head>
</head>
<body bgcolor="#FFFFFF">
<div class="navbar">
<a href="#home">Home</a>
<a href="#teaching">Teaching</a>
<a href="#research">Research</a>
</div>
<div class="navbar">
<a href="#home">Home</a>
<a href="#teaching">Teaching</a>
<a href="#research">Research</a>
<a href="#service">Service</a>
<a href="" onclick="toggleDarkLight();return false"><i id="toggleICON" class="fas fa-moon"></i></a>
</div>
<div class="main" id="home">
<p> </p><br>
</div>
<div class="main" id="home">
<p> </p><br>
</div>
<h1>YANG, Chen</h1>
<div id="shadowbox">
<table>
<tbody>
<tr>
<td width="10"></td>
<td width="160"><img src="ME.jpeg" width="160"></td>
<td width="20"></td>
<td>
Assistant Professor <br>
<a href="http://www.se.cuhk.edu.hk" target="_blank">Department of Systems Engineering and Engineering Management</a> <br>
<a href="https://www.erg.cuhk.edu.hk/erg/">Faculty of Engineering</a> <br>
The Chinese University of Hong Kong <br><br>
<i class="fas fa-map-marker-alt"></i>
&nbsp;&nbsp;Room 511A, William M.W. Mong Engineering Building <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The Chinese University of Hong Kong <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Shatin, N.T., Hong Kong<br><br>
<i class="fas fa-envelope"></i> &nbsp;cyang at se.cuhk.edu.hk <br>
<i class="fas fa-phone-alt"></i> &nbsp;+852 3943-8322 <br>
</td>
</tr>
</tbody>
</table>
</div>
<h1>YANG, Chen</h1>
<div>
<table class="isPrinttable">
<tbody>
<tr>
<td class="isPrint" width="5"></td>
<td class="isPrint" width="160"><img src="ME.jpeg" width="150"></td>
<td class="isPrint" width="20"></td>
<td>
<div class="isPrinttd">
Associate Professor <br>
<a class="extlink" href="http://www.se.cuhk.edu.hk" target="_blank">Department of Systems Engineering and
Engineering Management</a> <br>
<a class="extlink" href="https://www.erg.cuhk.edu.hk/erg/">Faculty of Engineering</a> <br>
The Chinese University of Hong Kong <br><br>
</div>
<i class="fas fa-map-marker-alt"></i>
<span class="links">&nbsp;&nbsp;</span>Room 511A, William M.W. Mong Engineering Building <br>
<span class="links">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>The Chinese University of Hong Kong <br>
<span class="links">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Shatin, N.T., Hong Kong<br>
<i class="fas fa-envelope"></i> &nbsp;cyang at se.cuhk.edu.hk <br>
<i class="fas fa-phone-alt"></i> &nbsp;+852 3943-8322 <br>
</td>
</tr>
</tbody>
</table>
</div>
<br>
<br><br>
<p>
<h3 id="teaching">Teaching <br> <a href="https://blackboard.cuhk.edu.hk" target="_blank">[Blackboard@CUHK]</a></h3>
Undergraduate Courses
<ul class="notATable">
<li><label><b>Spring 2023 </b></label><div>SEEM3580 Risk Analysis for Financial Engineering</div></li>
<li><label><b>Fall 2022 </b></label><div>SEEM3590 Investment Science</div></li>
<li><label><b>Spring 2022 </b></label><div>SEEM3580 Risk Analysis for Financial Engineering</div></li>
<li><label><b>Fall 2021 </b></label><div>SEEM3590 Investment Science</div></li>
<li><label><b>Spring 2021 </b></label><div>SEEM3580 Risk Analysis for Financial Engineering</div></li>
<li><label><b>Fall 2020 </b></label><div>SEEM3590 Investment Science</div></li>
<li><label><b>Spring 2020 </b></label><div>SEEM3580 Risk Analysis for Financial Engineering</div></li>
<li><label><b>Fall 2019 </b></label><div>SEEM3590 Investment Science</div></li>
</ul>
<hr id="teaching" class="style-one">
Postgraduate Courses
<ul class="notATable">
<li><label><b>Spring 2023 </b></label><div>SEEM5670 Advanced Models in Financial Engineering</div></li>
<li><label><b>Fall 2021 </b></label><div>SEEM5340 Stochastic Calculus (with <a href="https://sites.google.com/site/xuedonghepage/home" target="_blank">Xuedong He</a> and <a href="https://sites.google.com/site/lingfeilicuhk/" target="_blank">Lingfei Li</a>)</div></li>
</ul>
</p>
<hr class="style-one">
<p>
<h3>Teaching <br> <a id="blackboard" class="extlink" href="https://blackboard.cuhk.edu.hk" target="_blank">[Blackboard@CUHK]</a></h3>
Undergraduate Courses
<ul class="notATable">
<li><label><b>Spring 2020-2025 </b></label>
<div>SEEM3580 Risk Analysis for Financial Engineering</div>
</li>
<li><label><b>Fall 2019-2025 </b></label>
<div>SEEM3590 Investment Science</div>
</li>
</ul>
<p>
<h3 id="research">Research Interest</h3>
Stochastic Control; Market Frictions; Market Microstructure; FinTech; Deep Learning for Stochastic Control.
</p>
Postgraduate Courses
<ul class="notATable">
<li><label><b>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Spring 2025 </b></label>
<div>SEEM5410 Optimal Control</div>
</li>
<li><label><b>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Spring 2023 </b></label>
<div>SEEM5670 Advanced Models in Financial Engineering</div>
</li>
<li><label><b>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Fall 2021 </b></label>
<div>SEEM5340 Stochastic Calculus</div>
</li>
</ul>
</p>
<hr id="research" class="style-one">
<hr class="style-one">
<p>
<h3>Research Interest</h3>
<ul style="list-style-type:square">
<li> Portfolio Selection </li>
<li> Market Frictions and Microstructure (Capital Gains Tax, Price Impact, Transaction Costs) </li>
<li> FinTech (Decentralized Exchanges, Stablecoins, DeFi Lending) </li>
<li> Stochastic Control </li>
</ul>
</p>
<p>
<h3>Selected Publications</h3>
<ul style="list-style-type:square">
<li><b>Non-Concave Utility Maximization with Transaction Costs</b> (with <a href="https://sites.google.com/view/shuaijie-qian" target="_blank">Shuaijie Qian</a>).<br>
submitted. [<a href="" onclick="toggleAbstract('abs_NonconcaveTC');return false">Abstract</a>|<a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4500965" target="_blank">SSRN</a>|<a href="https://arxiv.org/abs/2307.02178" target="_blank">arXiv</a>]<br>
<div style="display:none" id="abs_NonconcaveTC">
<hr>
<i>This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs. The commonly used concavification principle for terminal value is no longer valid here, and we establish a proper theoretical characterization of this problem. We first give the asymptotic terminal behavior of the value function, which implies any transaction close to maturity only provides a marginal contribution to the utility. After that, the theoretical foundation is established in terms of a novel definition of the viscosity solution incorporating our asymptotic terminal condition. Via numerical analyses, we find that the introduction of transaction costs into non-concave utility maximization problems can prevent the portfolio from unbounded leverage and make a large short position in stock optimal despite a positive risk premium and symmetric transaction costs.</i>
</div>
</li><br>
<hr class="style-one">
<li><b>Optimal Investment under Block-Shaped Order Books</b> (with <a href="https://www1.se.cuhk.edu.hk/~nchenweb/index.htm" target="_blank">Nan Chen</a>, <a href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a>, and Qiheng Ding).<br>
working paper. [<a href="" onclick="toggleAbstract('abs_LOB');return false">Abstract</a>]<br>
<div style="display:none" id="abs_LOB">
<hr>
<i>We study an optimal investment problem of a CARA investor trading in a market operated with a block-shaped limited order book (LOB). The model synergizes three key features of market microstructure: the bid-ask spread, the market depth, and a finite market resilience. Under a Bachelier process for the dynamic of the fundamental value of the asset, we develop explicit characterization on the investors optimal trading strategy. As an important extension of this model, an asymptotic expansion of the optimal trading strategies in the presence of return-predicting signals are also derived. The theoretical and numerical results unveil how an investor should strike a balance among several competing goals such as achieving the optimal risk exposure currently, incorporating signals about the future, and minimizing trading costs. Contributing to the existing literature, our model helps to quantify significant impacts of the market resilience on the trading decisions. </i>
</div>
</li><br>
<p>
<h3>Selected Publications</h3>
<ol>
<li>Optimal Investment with Quadratic Transaction Costs in a Multi-factor and Stochastic Interest Rate Environment (with <a class="authorlink" href="https://sites.google.com/view/lingfeili/home"
target="_blank">Lingfei Li</a> and Qianyu Liu).<br>
Working Paper. <span class="links">[<a class="paperlink" href="" onclick="toggleAbstract('abs_investFactor');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5652190" target="_blank">SSRN</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_investFactor">
<hr>
This paper studies an optimal investment problem in a comprehensive market environment featuring geometric Brownian motion type asset dynamics, stochastic interest rates, return and volatility factors, and time-varying, state-dependent quadratic transaction costs. Under a finite-horizon mean-quadratic variation objective, we derive a semi-analytical solution for the value function and optimal trading strategy and establish the well-posedness of the associated system of nonlinear PDEs along with the verification theorem. The optimal strategy retains a tractable structure that echoes the core economic principle of trading gradually toward an aim portfolio as proposed in Gârleanu and Pedersen (2013). Specifically, the aim portfolio is adjusted for hedging demands against the interest rate risk, and the trading speed reflects an intertemporal trade-off between immediate rebalancing costs and future market liquidity. Additionally, we propose a deep learning scheme to enable efficient implementation in high-dimensional settings based on observable market data and estimated factor models.
</div>
</li><br>
<li>Arbitrage on Decentralized Exchanges (with <a class="authorlink" href="https://sites.google.com/site/xuedonghepage/home"
target="_blank">Xuedong He</a> and <a class="authorlink" href="https://hk.linkedin.com/in/yutian-zhou-555870189" target="_blank">Yutian Zhou</a>).<br>
Working Paper. <span class="links">[<a class="paperlink" href="" onclick="toggleAbstract('abs_arbDEX');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5347630" target="_blank">SSRN</a>|<a class="paperlink" href="https://arxiv.org/abs/2507.08302" target="_blank">arXiv</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_arbDEX">
<hr>
Decentralized exchanges (DEXs) are alternative venues to centralized exchanges (CEXs) for trading
cryptocurrencies and have become increasingly popular. An arbitrage opportunity arises when
the exchange rate of two cryptocurrencies in a DEX differs from that in a CEX. Arbitrageurs can then
trade on the DEX and CEX to make a profit. Trading on the DEX incurs a gas fee, which determines the
priority of the trade being executed. We study a gas-fee competition game between two arbitrageurs
who maximize their expected profit from trading. We derive the unique symmetric mixed Nash
equilibrium and find that (i) the arbitrageurs may choose not to trade when the arbitrage
opportunity is small; (ii) the probability of the arbitrageurs choosing a higher gas fee is lower;
(iii) the arbitrageurs pay a higher gas fee and trade more when the arbitrage opportunity becomes
larger and when liquidity becomes higher. The above findings are consistent with our empirical
study.
</div>
</li><br>
<li><b>Designing Stable Coins</b> (with <a href="https://www.linkedin.com/in/yizhoucao/" target="_blank">Yizhou Cao</a>, <a href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a>, <a href="https://www.bu.edu/questrom/profile/steven-kou/" target="_blank">Steven Kou</a> and <a href="https://www.linkedin.com/in/lewei-li/" target="_blank">Lewei Li</a>).<br>
submitted. [<a href="" onclick="toggleAbstract('abs_StableCoin');return false">Abstract</a>|<a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3856569" target="_blank">SSRN</a>]<br>
<div style="display:none" id="abs_StableCoin">
<hr>
<i>Stable coins, which are cryptocurrencies pegged to other stable financial assets such as U.S. dollar, are desirable for payments within blockchain networks, whereby being often called the “Holy Grail of cryptocurrency.” However, existing cryptocurrencies are too volatile for these purposes. By using the option pricing theory, we design several dual-class structures that offer a fixed income crypto asset, a stable coin pegged to a traditional currency, and leveraged investment instruments. To understand the impact of the proposed coins on the speculative and non-speculative demands of cryptocurrencies, we study equilibrium with and without the stable coins. Our investigation of the values of stable coins in presence of jump risk and black-swan type events shows the robustness of the design.</i>
</div>
</li><br>
<li>Periodic Evaluation with Non-Concave Utility (with <a class="authorlink"
href="https://scholar.google.com/citations?user=OzeF8T0AAAAJ&hl" target="_blank">Cong Qin</a> and <a class="authorlink"
href="https://www.ma.ic.ac.uk/~hz/"> Harry Zheng</a>).<br>
submitted. <span class="links">[<a class="paperlink" href=""
onclick="toggleAbstract('abs_periodicEvaluation');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5305617" target="_blank">SSRN</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_periodicEvaluation">
<hr>
A fund manager's performance is often evaluated annually and compared with a benchmark, such as a
market index. In addition, the manager may be subject to trading constraints, such as limited use of
leverage, no short-selling, and a forced liquidation clause. We formulate this as a periodic
evaluation problem with a non-concave utility, a stochastic reference point, and trading
constraints. The value function is characterized as the unique solution to a Hamilton-Jacobi-Bellman
equation with periodic terminal and boundary conditions, which must be imposed carefully due to
possible discontinuities at the terminal time and/or on the liquidation boundary. We find that, at
the evaluation time, future investment opportunities induce a discontinuity in the value function on
the liquidation boundary, leading to a substantial change in local risk-aversion. More importantly,
this local concavity/convexity weakens and shifts inward from the liquidation boundary to the
interior region as the evaluation horizon increases. As a result, the joint effect of periodic
evaluation and forced liquidation can generate highly nonlinear investment strategies, which is
helpful in understanding the complexity of trading strategies in the loss region.
</div>
</li><br>
<li><b>An Equilibrium Model for the Cross-Section of Liquidity Premia</b> (with <a href="https://wwwf.imperial.ac.uk/~jmuhleka/" target="_blank">Johannes Muhle-Karbe</a> and <a href="https://xf-shi.github.io" target="_blank">Xiaofei Shi</a>).<br>
<i>Mathematics of Operations Research</i>, forthcoming. [<a href="" onclick="toggleAbstract('abs_LiqPre');return false">Abstract</a>|<a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3738500" target="_blank">SSRN</a>|<a href="https://arxiv.org/abs/2011.13625"
target="_blank">arXiv</a>|<a href="https://pubsonline.informs.org/doi/abs/10.1287/moor.2022.1307" target="_blank">Article</a>]<br>
<div style="display:none" id="abs_LiqPre">
<hr>
<i>We study a risk-sharing economy where an arbitrary number of heterogenous agents trades an arbitrary number of risky assets subject to quadratic transaction costs. For linear state dynamics, the forward-backward stochastic differential equations characterizing equilibrium asset prices and trading strategies in this context reduce to a system of matrix-valued Riccati equations. We prove the existence of a unique global solution and provide explicit asymptotic expansions that allow us to approximate the corresponding equilibrium for small transaction costs. These tractable approximation formulas make it feasible to calibrate the model to time series of prices and trading volume, and to study the cross-section of liquidity premia earned by assets with higher and lower trading costs. This is illustrated by an empirical case study.</i>
</div>
</li><br>
<li><b>Leveraged Exchange-Traded Funds with Market Closure and Frictions</b> (with <a href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a>, <a href="https://www.bu.edu/questrom/profile/steven-kou/" target="_blank">Steven Kou</a> and <a href="https://people.math.ethz.ch/~hmsoner/" target="blank">H. Mete Soner</a>).<br>
<i>Management Science</i>, 69(4):1935-2545, 2023. [<a href="" onclick="toggleAbstract('abs_LETF');return false">Abstract</a>|<a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3856573" target="_blank">SSRN</a>|<a href="https://pubsonline.informs.org/doi/abs/10.1287/mnsc.2022.4407" target="_blank">Article</a>]<br>
<div style="display:none" id="abs_LETF">
<hr>
<i>Although leveraged ETFs are popular products for retail investors, how to hedge them poses a great challenge to financial institutions. We develop an optimal rebalancing (hedging) model for leveraged ETFs in a comprehensive setting, including overnight market closure and market frictions. The model allows for an analytical optimal rebalancing strategy.
The result extends the principle of "aiming in front of target" introduced by <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/jofi.12080" target="_black">G&acirc;rleanu and Pedersen (2013)</a> from a constant weight between current and future positions to a time-varying weight, because the rebalancing performance is monitored only at discrete time points but the rebalancing takes place continuously. Empirical findings and implications for the weekend effect and the intraday trading volume are also presented.</i>
</div>
</li><br>
<li>Pricing Model for Data Assets in Investment-Consumption Framework with Ambiguity (with <a class="authorlink"
href="https://scholar.google.com/citations?user=os0TtfkAAAAJ&hl=en" target="_blank">Xiaoshan Chen</a>
and <a class="authorlink" href="https://www.researchgate.net/profile/Zhou-Yang-9" target="_blank">Zhou Yang</a>).<br>
submitted. <span class="links">[<a class="paperlink" href="" onclick="toggleAbstract('abs_dataAsset');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5263455" target="_blank">SSRN</a>|<a class="paperlink"
href="https://arxiv.org/abs/2505.16106" target="_blank">arXiv</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_dataAsset">
<hr>
Data assets are data commodities that have been processed, produced, priced, and traded based on
actual demand. Reasonable pricing mechanism for data assets is essential for developing the data
market and realizing their value. Most existing literature approaches data asset pricing from the
seller's perspective, focusing on data properties and collection costs, however, research from the
buyer's perspective remains scarce. This gap stems from the nature of data assets: their value lies
not in direct revenue generation but in providing informational advantages that enable enhanced
decision-making and excess returns. This paper addresses this gap by developing a pricing model
based on the informational value of data assets from the buyer's perspective. We determine data
asset prices through an implicit function derived from the value functions in two robust
investment-consumption problems under ambiguity markets via indifference pricing principle. By the
existing research results, we simplify the value function, using mathematical analysis and
differential equation theory, we derive general expressions for data assets price and explore their
properties under various conditions. Furthermore, we derive the explicit pricing formulas for
specific scenarios and provide numerical illustration to describe how to use our pricing model.
</div>
</li><br>
<li><b>A Stochastic Representation for Nonlocal Parabolic PDEs with Applications</b> (with <a href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a> and <a href="https://www.bu.edu/questrom/profile/steven-kou/" target="_blank">Steven Kou</a>).<br>
<i>Mathematics of Operations Research</i>, 47(3):1707-2545, 2022 [<a href="" onclick="toggleAbstract('abs_FK');return false">Abstract</a>|<a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3541591" target="_blank">SSRN</a>|<a href="https://pubsonline.informs.org/doi/abs/10.1287/moor.2020.1061" target="_blank">Article</a>]<br>
<div style="display:none" id="abs_FK">
<hr>
<i>We establish a stochastic representation for a class of nonlocal parabolic terminal-boundary value problems, whose terminal and boundary conditions depend on the solution in the interior domain; in particular, the solution is represented as the expectation of functionals of a diffusion process with random jumps from boundaries. We discuss three applications of the representation, the first one on the pricing of dual-purpose funds, the second one on the connection to regenerative processes, and the third one on modeling the entropy on a one-dimensional non-rigid body.</i>
</div>
</li><br>
<li>Arbitrage in Perpetual Contracts (with <a class="authorlink" href="https://sites.google.com/view/mindai/home"
target="_blank">Min Dai</a> and <a class="authorlink" href="https://sg.linkedin.com/in/linfeng-li-263843184" target="_blank">Linfeng Li</a>).<br>
submitted. Updated: September 2025. <span class="links">[<a class="paperlink" href="" onclick="toggleAbstract('abs_arbPerp');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5262988" target="_blank">SSRN</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_arbPerp">
<hr>
Perpetual contracts, designed to track the underlying price through a funding swap mechanism, have
gained significant popularity in cryptocurrency markets. However, observed price discrepancies
between perpetual contracts and the underlying asset cannot be explained solely by transaction fees.
By examining the impact of the clamping function inherent in the funding swap mechanism -- an
overlooked aspect in existing literature -- we derive model-free no-arbitrage bounds for perpetual
contracts. Our findings reveal that these bounds persist as intervals even without transaction fees,
due to the clamping function. Empirical analysis using two years of Binance data supports the
validity of our proposed bounds.
</div>
</li><br>
<li><b>Inventory Management for High-Frequency Trading with Imperfect Competition</b> (with <a href="http://www-personal.umich.edu/~sherrma/" target="blank">Sebastian Herrmann</a>, <a href="https://wwwf.imperial.ac.uk/~jmuhleka/" target="blank">Johannes Muhle-Karbe</a> and <a href="https://www.linkedin.com/in/dapeng-shang-654316105/<Paste>" target="blank">Dapeng Shang</a>).<br>
<i>SIAM Journal on Financial Mathematics</i>, 11(1):1-26, 2020. [<a href="" onclick="toggleAbstract('abs_HFT');return false">Abstract</a>|<a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3232037" target="_blank">SSRN</a>|<a href="http://arxiv.org/abs/1808.05169" target="_blank">arXiv</a>|<a href="https://epubs.siam.org/doi/abs/10.1137/18M1207776" target="_blank">Article</a>]<br>
<div style="display:none" id="abs_HFT">
<hr>
<i>We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain around the continuous-time limit. Unlike in the risk-neutral case, the optimal inventories become mean-reverting and vanish as the number of trading rounds becomes large. In contrast, the HFTs' risk-adjusted profits and the equilibrium price impact converge to their risk-neutral counterparts. Compared to a social-planner solution for cooperative HFTs, Nash competition leads to excess trading, so that marginal transaction taxes in fact decrease market liquidity.</i>
</div>
</li><br>
<li>Optimal Design of Automated Market Makers on Decentralized Exchanges (with <a class="authorlink"
href="https://sites.google.com/site/xuedonghepage/home" target="_blank">Xuedong He</a> and <a class="authorlink" href="https://hk.linkedin.com/in/yutian-zhou-555870189" target="_blank">Yutian Zhou</a>).<br>
submitted. <span class="links">[<a class="paperlink" href="" onclick="toggleAbstract('abs_AMM');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4801468" target="_blank">SSRN</a>|<a class="paperlink"
href="https://arxiv.org/abs/2404.13291" target="_blank">arXiv</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_AMM">
<hr>
Automated market makers are a popular mechanism used on decentralized exchange, through which users
trade assets with each other directly and automatically through a liquidity pool and a fixed pricing
function. The liquidity provider contributes to the liquidity pool by supplying assets to the pool,
and in return, they earn trading fees from investors who trade in the pool. We propose a model of
optimal liquidity provision in which a risk-averse liquidity provider decides the amount of wealth
she would invest in the decentralized market to provide liquidity in a two-asset pool, trade in a
centralized market, and consume in multiple periods. We derive the liquidity provider's optimal
strategy and the optimal design of the automated market maker that maximizes the liquidity
provider's utility. We find that the optimal unit trading fee increases in the volatility of the
fundamental exchange rate of the two assets. We also find that the optimal pricing function is
chosen to make the asset allocation in the liquidity pool efficient for the liquidity provider.
</div>
</li><br>
<li><b>Optimal Tax-timing with Asymmetric Long-term/short-term Capital Gains Tax</b> (with <a href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a>, <a href="http://apps.olin.wustl.edu/faculty/liuh/" target="blank">Hong Liu</a> and <a href="https://www.linkedin.com/in/yifei-zhong-12858524/" target="_blank">Yifei Zhong</a>).<br>
<i>The Review of Financial Studies</i> 28.9:2687-2721, 2015. [<a href="" onclick="toggleAbstract('abs_taxTiming');return false">Abstract</a>|<a href=https://academic.oup.com/rfs/article/28/9/2687/1581078, target="_blank">Article</a>]<br>
<div style="display:none" id="abs_taxTiming">
<hr>
<i>We develop an optimal tax-timing model that takes into account asymmetric long-term and short-term tax rates for positive capital gains and limited tax deductibility of capital losses. In contrast to the existing literature, this model can help explain why many investors not only defer short-term capital losses to long term but also defer large long-term capital gains and losses. Because the benefit of tax deductibility of capital losses increases with the short-term tax rates, effective tax rates can decrease as short-term capital gains tax rates increase.</i>
</div>
</li>
</ul>
</p>
<li>Calibration of Local Volatility Models under the Implied Volatility Criterion (with <a class="authorlink"
href="https://scholar.google.com/citations?user=MbbX8kUAAAAJ&hl=en" target="_blank">Xinfu Chen</a>, <a class="authorlink"
href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a>, and <a class="authorlink" href="https://www.researchgate.net/profile/Zhou-Yang-9" target="_blank">Zhou Yang</a>).<br>
submitted. <span class="links">[<a class="paperlink" href="" onclick="toggleAbstract('abs_LocalVol');return false">Abstract</a>|<a class="paperlink"
href=" https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4801520" target="_blank">SSRN</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_LocalVol">
<hr>
We study non-parametric calibration of local volatility models, which is formulated as an inverse
problem of partial differential equations with Tikhonov regularization. In contrast to the existing
literature minimizing the distance between theoretical and market prices of options as a calibration
criterion, we instead minimize the distance between theoretical and market implied volatilities,
complying with market practices. We prove that our calibration criterion naturally leads to the
well-posedness of the calibration problem. In particular, comparing to Jiang and Tao (2001), we
obtain a global uniqueness result, where no additional weight functions are required. Numerical
results reveal that our method achieves a better trade-off between minimizing calibration errors and
reducing overfitting.
</div>
</li><br>
<hr class="style-one">
<p>
<h3>Grants</h3>
<ul style="list-style-type:square">
<li> General Research Fund (ECS), <i>High-Dimensional Continuous-Time Portfolio Selection with Capital Gains Tax</i>, 2022 - 2024</li>
<li> Direct Grant, <i>Hedging Periodic Cash Flow Streams under Market Frictions</i>, 2020 - 2022 </li>
<li> Start-up Grant at CUHK </li>
</ul>
</p>
<li>Patience is a Virtue: Optimal Investment in the Presence of Market Resilience (with <a class="authorlink"
href="https://www1.se.cuhk.edu.hk/~nchenweb/index.htm" target="_blank">Nan Chen</a>, <a class="authorlink"
href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a>, and Qiheng Ding).<br>
submitted. Updated: July 2025. <span class="links">[<a class="paperlink" href="" onclick="toggleAbstract('abs_LOB');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4671774" target="_blank">SSRN</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_LOB">
<hr>
This paper investigates an optimal investment problem in an illiquid market, modeling explicitly the
effects of three key features of market microstructure --- market tightness, market depth, and
finite market resilience --- on the investor's decision. By employing a Bachelier process to model
the dynamic of the fundamental value of the asset and assuming CARA-type utility for the investor,
we obtain the investor's optimal dynamic trading strategy in closed form by solving the
resulting high-dimensional singular control problem. Furthermore, we extend the model to incorporate
return-predicting signals and utilize an asymptotic expansion approach to derive approximate optimal
trading strategies. The theoretical and numerical results emphasize the vital role of patience.
Specifically, rather than dispersing small trades continuously over time as advocated by the
existing literature, our findings suggest that investors should strategically time their trading
activities jointly based on market liquidity and market signal. To quantify this
timing decision, we introduce a patience index that enables investors to strike a balance among
various competing goals, including achieving currently optimal risk exposure, incorporating signals
about future predictions, and minimizing trading costs, by leveraging market resilience. We also
demonstrate how to implement our patient trading strategy using real-life market data.
</div>
</li><br>
<hr class="style-one">
<li>Non-Concave Utility Maximization with Transaction Costs (with <a class="authorlink"
href="https://sites.google.com/view/shuaijie-qian" target="_blank">Shuaijie Qian</a>).<br>
<i><b>SIAM Journal on Financial Mathematics</b></i>. <i>Accepted for Publication</i>. <span class="links">[<a class="paperlink" href="" onclick="toggleAbstract('abs_NonconcaveTC');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4500965" target="_blank">SSRN</a>|<a class="paperlink"
href="https://arxiv.org/abs/2307.02178" target="_blank">arXiv</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_NonconcaveTC">
<hr>
This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and
proportional transaction costs. The commonly used concavification principle for terminal value is no
longer valid here, and we establish a proper theoretical characterization of this problem. We first
give the asymptotic terminal behavior of the value function, which implies any transaction close to
maturity only provides a marginal contribution to the utility. After that, the theoretical
foundation is established in terms of a novel definition of the viscosity solution incorporating our
asymptotic terminal condition. Via numerical analyses, we find that the introduction of transaction
costs into non-concave utility maximization problems can prevent the portfolio from unbounded
leverage and make a large short position in stock optimal despite a positive risk premium and
symmetric transaction costs.
</div>
</li><br>
<p>
<h3>Professional Service</h3>
<ul style="list-style-type:square">
<li> <b>Associate Editor:</b> <a href="https://www.springer.com/journal/42521" target="_blank"><i>Digital Finance</i></a>, 2020 - Present</li>
<li> <b>Reviewer:</b> Operations Research, Management Science, Mathematical Finance, Mathematics of Operations Research, SIAM Journal on Financial Mathematics, Quantitative Finance, Mathematics and Financial Economics. </li>
<li> <b>Conference Organizer:</b>
<ul style="list-style-type:circle">
<li> Mini-Symposium Organizer, <a href="https://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=70910" target="_blank"><b>MS5 Investment and Asset Pricing under Market Frictions</b></a>, SIAM Conference on Financial Mathematics and Engineering (FM21), 2021. </li>
<li> Invited Session Chair, <b>Financial Frictions and Machine Learning</b><a>, 2023 INFORMS Annual Meeting, 2023. </li>
</ul>
</li>
<li> <b>I am one of the organizers of <a href="https://sites.google.com/view/hksgfinmatheng/home" target="_blank"><b>The Hong Kong - Singapore Joint Seminar Series in Financial Mathematics/Engineering.</b><a></li>
</ul>
</p>
<li>Optimal Tax-Timing with Transaction Costs (with <a class="authorlink" href="https://sites.google.com/view/mindai/home"
target="_blank">Min Dai</a>, Yaoting Lei, and <a class="authorlink" href="http://apps.olin.wustl.edu/faculty/liuh/"
target="blank">Hong Liu</a>).<br>
<i><b>Management Science</b></i>, <i>Accepted for Publication</i>. <span class="links">[<a class="paperlink" href="" onclick="toggleAbstract('abs_TaxTC');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4952040" target="_blank">SSRN</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_TaxTC">
<hr>
We develop a dynamic portfolio model incorporating capital gains tax (CGT), transaction costs, and
year-end taxation. We find that even tiny transaction costs can lead to significant deferral of
large losses and transaction costs affect loss deferrals much more than gain deferrals. Our model
can thus help explain the puzzle that even when investors face equal long-term/short-term CGT rates,
they may still defer realizing large capital losses for an extended period of time, displaying the
disposition effect. In addition, we find misestimating transaction costs is costly. We also provide
several unique, empirically testable predictions and shed light on recently proposed tax policy
changes.
</div>
</li><br>
<hr class="curve">
<li>Designing Stablecoins (with <a class="authorlink" href="https://www.linkedin.com/in/yizhoucao/" target="_blank">Yizhou Cao</a>,
<a class="authorlink" href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a>, <a class="authorlink"
href="https://www.bu.edu/questrom/profile/steven-kou/" target="_blank">Steven Kou</a> and <a class="authorlink"
href="https://www.linkedin.com/in/lewei-li/" target="_blank">Lewei Li</a>).<br>
<i><b>Mathematical Finance</b></i>, 35(1):263-294, 2025. <span class="links">[<a class="paperlink" href=""
onclick="toggleAbstract('abs_StableCoin');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3856569" target="_blank">SSRN</a>|<a class="paperlink"
href="https://doi.org/10.1111/mafi.12445" target="_blank">Article</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_StableCoin">
<hr>
Stable coins, which are cryptocurrencies pegged to other stable financial assets such as U.S. dollar,
are desirable for payments within blockchain networks, whereby being often called the “Holy Grail of
cryptocurrency.” However, existing cryptocurrencies are too volatile for these purposes. By using
the option pricing theory, we design several dual-class structures that offer a fixed income crypto
asset, a stable coin pegged to a traditional currency, and leveraged investment instruments. To
understand the impact of the proposed coins on the speculative and non-speculative demands of
cryptocurrencies, we study equilibrium with and without the stable coins. Our investigation of the
values of stable coins in presence of jump risk and black-swan type events shows the robustness of
the design.
</div>
</li><br>
<div align="right"><font size="-1"></font></div>
<li>An Equilibrium Model for the Cross Section of Liquidity Premia (with <a class="authorlink"
href="https://wwwf.imperial.ac.uk/~jmuhleka/" target="_blank">Johannes Muhle-Karbe</a> and <a class="authorlink"
href="https://xf-shi.github.io" target="_blank">Xiaofei Shi</a>).<br>
<i><b>Mathematics of Operations Research</b></i>, 48(3):1423-1453, 2023. <span class="links">[<a class="paperlink" href=""
onclick="toggleAbstract('abs_LiqPre');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3738500" target="_blank">SSRN</a>|<a class="paperlink"
href="https://arxiv.org/abs/2011.13625" target="_blank">arXiv</a>|<a class="paperlink"
href="https://pubsonline.informs.org/doi/abs/10.1287/moor.2022.1307" target="_blank">Article</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_LiqPre">
<hr>
We study a risk-sharing economy where an arbitrary number of heterogenous agents trades an arbitrary
number of risky assets subject to quadratic transaction costs. For linear state dynamics, the
forward-backward stochastic differential equations characterizing equilibrium asset prices and
trading strategies in this context reduce to a system of matrix-valued Riccati equations. We prove
the existence of a unique global solution and provide explicit asymptotic expansions that allow us
to approximate the corresponding equilibrium for small transaction costs. These tractable
approximation formulas make it feasible to calibrate the model to time series of prices and trading
volume, and to study the cross-section of liquidity premia earned by assets with higher and lower
trading costs. This is illustrated by an empirical case study.
</div>
</li><br>
<li>Leveraged Exchange-Traded Funds with Market Closure and Frictions (with <a class="authorlink"
href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a>, <a class="authorlink"
href="https://www.bu.edu/questrom/profile/steven-kou/" target="_blank">Steven Kou</a> and <a class="authorlink"
href="https://people.math.ethz.ch/~hmsoner/" target="blank">H. Mete Soner</a>).<br>
<i><b>Management Science</b></i>, 69(4):2517-2535, 2023. <span class="links">[<a class="paperlink" href=""
onclick="toggleAbstract('abs_LETF');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3856573" target="_blank">SSRN</a>|<a class="paperlink"
href="https://pubsonline.informs.org/doi/abs/10.1287/mnsc.2022.4407" target="_blank">Article</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_LETF">
<hr>
Although leveraged ETFs are popular products for retail investors, how to hedge them poses a great
challenge to financial institutions. We develop an optimal rebalancing (hedging) model for leveraged
ETFs in a comprehensive setting, including overnight market closure and market frictions. The model
allows for an analytical optimal rebalancing strategy.
The result extends the principle of "aiming in front of target" introduced by <a class="paperlink"
href="https://onlinelibrary.wiley.com/doi/abs/10.1111/jofi.12080" target="_black">G&acirc;rleanu
and Pedersen (2013)</a> from a constant weight between current and future positions to a
time-varying weight, because the rebalancing performance is monitored only at discrete time points
but the rebalancing takes place continuously. Empirical findings and implications for the weekend
effect and the intraday trading volume are also presented.
</div>
</li><br>
<li>A Stochastic Representation for Nonlocal Parabolic PDEs with Applications (with <a class="authorlink"
href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a> and <a class="authorlink"
href="https://www.bu.edu/questrom/profile/steven-kou/" target="_blank">Steven Kou</a>).<br>
<i><b>Mathematics of Operations Research</b></i>, 47(3):1707-1730, 2022 <span class="links">[<a class="paperlink" href=""
onclick="toggleAbstract('abs_FK');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3541591" target="_blank">SSRN</a>|<a class="paperlink"
href="https://pubsonline.informs.org/doi/abs/10.1287/moor.2020.1061" target="_blank">Article</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_FK">
<hr>
We establish a stochastic representation for a class of nonlocal parabolic terminal-boundary value
problems, whose terminal and boundary conditions depend on the solution in the interior domain; in
particular, the solution is represented as the expectation of functionals of a diffusion process
with random jumps from boundaries. We discuss three applications of the representation, the first
one on the pricing of dual-purpose funds, the second one on the connection to regenerative
processes, and the third one on modeling the entropy on a one-dimensional non-rigid body.
</div>
</li><br>
<li>Inventory Management for High-Frequency Trading with Imperfect Competition (with <a class="authorlink"
href="http://www-personal.umich.edu/~sherrma/" target="blank">Sebastian Herrmann</a>, <a class="authorlink"
href="https://wwwf.imperial.ac.uk/~jmuhleka/" target="blank">Johannes Muhle-Karbe</a> and <a class="authorlink"
href="https://www.linkedin.com/in/dapeng-shang-654316105/" target="blank">Dapeng Shang</a>).<br>
<i><b>SIAM Journal on Financial Mathematics</b></i>, 11(1):1-26, 2020. <span class="links">[<a class="paperlink" href=""
onclick="toggleAbstract('abs_HFT');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3232037" target="_blank">SSRN</a>|<a class="paperlink"
href="http://arxiv.org/abs/1808.05169" target="_blank">arXiv</a>|<a class="paperlink"
href="https://epubs.siam.org/doi/abs/10.1137/18M1207776" target="_blank">Article</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_HFT">
<hr>
We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit
information about future price changes. For discrete trading rounds, the HFTs' optimal trading
strategies and their equilibrium price impact are described by a system of nonlinear equations;
explicit solutions obtain around the continuous-time limit. Unlike in the risk-neutral case, the
optimal inventories become mean-reverting and vanish as the number of trading rounds becomes large.
In contrast, the HFTs' risk-adjusted profits and the equilibrium price impact converge to their
risk-neutral counterparts. Compared to a social-planner solution for cooperative HFTs, Nash
competition leads to excess trading, so that marginal transaction taxes in fact decrease market
liquidity.
</div>
</li><br>
<li>Optimal Tax-timing with Asymmetric Long-term/short-term Capital Gains Tax (with <a class="authorlink"
href="https://sites.google.com/view/mindai/home" target="_blank">Min Dai</a>, <a class="authorlink"
href="http://apps.olin.wustl.edu/faculty/liuh/" target="blank">Hong Liu</a> and <a class="authorlink"
href="https://www.linkedin.com/in/yifei-zhong-12858524/" target="_blank">Yifei Zhong</a>).<br>
<i><b>The Review of Financial Studies</b></i>, 28.9:2687-2721, 2015. <span class="links">[<a class="paperlink" href=""
onclick="toggleAbstract('abs_taxTiming');return false">Abstract</a>|<a class="paperlink"
href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1786012" target="_blank">SSRN</a>|<a class="paperlink"
href=https://academic.oup.com/rfs/article/28/9/2687/1581078, target="_blank">Article</a>]</span><br>
<div class="fade-in" style="display:none" id="abs_taxTiming">
<hr>
We develop an optimal tax-timing model that takes into account asymmetric long-term and short-term
tax rates for positive capital gains and limited tax deductibility of capital losses. In contrast to
the existing literature, this model can help explain why many investors not only defer short-term
capital losses to long term but also defer large long-term capital gains and losses. Because the
benefit of tax deductibility of capital losses increases with the short-term tax rates, effective
tax rates can decrease as short-term capital gains tax rates increase.
</div>
</li>
</ol>
</p>
<hr class="style-one">
<p>
<h3>Grants</h3>
<ul style="list-style-type:square">
<li> General Research Fund, <i>Continuous-Time Nonconcave Portfolio Selection with General Payoffs and
Transaction Costs</i>, 2023 - 2026</li>
<li> General Research Fund (ECS), <i>High-Dimensional Continuous-Time Portfolio Selection with Capital Gains
Tax</i>, 2022 - 2024</li>
<li> Direct Grant, <i>Hedging Periodic Cash Flow Streams under Market Frictions</i>, 2020 - 2022 </li>
<li> Start-up Grant at CUHK </li>
</ul>
</p>
<hr id="service" class="style-one">
<p>
<h3>Professional Service</h3>
<ul style="list-style-type:square">
<li> <b>Associate Editor:</b> <a class="jourlink" href="https://www.springer.com/journal/42521" target="_blank"><i><b>Digital
Finance</b></i></a>, 2020 - Present</li><br>
<li> <b>Reviewer:</b>
<ul style="list-style-type:circle">
<li> Management Science, Operations Research, Mathematics of Operations Research, Journal of the Operational Research Society, Journal of Optimization Theory and Applications</li>
<li> Mathematical Finance, Finance and Stochastics, SIAM Journal on Financial Mathematics, Quantitative
Finance, Mathematics and Financial Economics. </li>
<li> Journal of Financial and Quantitative Analysis, European Financial Management, Journal of Economic Dynamics and Control, International Journal of
Theoretical and Applied Finance, Economic Modelling. </li>
</ul>
</li><br>
<li> <b>Conference Organizing:</b>
<ul style="list-style-type:circle">
<li> Local Organizing Committee Member, <a class="jourlink" href="https://events.polyu.edu.hk/scftml/home"
target='_blank'><b>Workshop on Stochastic Control, Financial Technology, and Machine Learning</b></a>, 2025</li>
<li> Mini-Symposium Organizer, <a class="jourlink" href="https://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=84092"
target='_blank'><b>MS54 Recent Advances in Quantitative Finance and FinTech</b></a>, SIAM
Conference on Financial Mathematics and Engineering (FM25), 2025.</li>
<li> Session Chair, <b>ME14 Quantitative Finance and FinTech</b>, 2024 INFORMS Annual Meeting, 2024.
</li>
<li> Local Organizing Committee Member, <a class="jourlink" href="https://events.polyu.edu.hk/icfe/home"
target='_blank'><b>First INFORMS Conference on Financial Engineering and FinTech</b></a>, 2024. </li>
<li> Session Chair, <b>TA73 Financial Frictions and Machine Learning</b>, 2023 INFORMS Annual Meeting,
2023. </li>
<li> Local Organizing Committee Member, <a class="jourlink"
href="https://www.polyu.edu.hk/ama/news-and-events/events/2023/8/recent-advances-on-quantitative-finance/"
target="_blank"><b>Recent Advances on Quantitative Finance</b></a>, 2023. </li>
<li> Mini-Symposium Organizer, <a class="jourlink"
href="https://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=70910"
target="_blank"><b>MS5 Investment and Asset Pricing under Market Frictions</b></a>, SIAM
Conference on Financial Mathematics and Engineering (FM21), 2021. </li>
</ul>
</li><br>
<li> <b> Seminar Organizing:</b>
<ul style="list-style-type:circle">
<li> Organizing Committee Member, <a class="extlink" href="https://sites.google.com/view/hksgfinmatheng/home"
target="_blank"><b>The Hong Kong - Singapore Joint Seminar Series in Financial
Mathematics/Engineering</b></a>.</li>
<li> Organizing Committee Member, <a class="extlink" href="https://www.cfe.cuhk.edu.hk/cuhkqf/" target="_blank"><b>CUHK
Distinguished Lectures in Quantitative Finance</b></a>.</li>
</ul>
</li>
</ul>
</p>
<div align="right">
<font size="-1"></font>
</div>
<div class="container">
<div class="ball"></div>
<div class="ball"></div>
<div class="ball"></div>
<div class="ball"></div>
<div class="ball"></div>
<div class="ball"></div>
<div class="ball"></div>
</div>
</body>
</html>

323
style-print.css Executable file
View File

@@ -0,0 +1,323 @@
html {
scroll-behavior: smooth;
max-width: 50em;
margin: 1cm;
}
body {
font-family: "Palatino", "Georgia", Times, serif;
background-color: white;
color: black;
line-height: 1.2;
/* padding-bottom: 12.5em; */
font-size: 10pt;
}
.main {
display: none;
}
img {
border-radius: 1em;
display: none;
}
.isPrint {
display: none;
}
.isPrinttd {
text-align: center;
width: auto;
}
.isPrinttable {
margin:0 auto;
text-align: center;
}
h1 {
text-align: center;
}
h2,
h3,
h4 {
padding-top: 0em;
padding-bottom: 0em;
text-align: left;
}
th {
font-weight: normal;
}
a {
color: black;
}
.authorlink {
color: black;
text-decoration: none;
}
.paperlink {
color: #9d0006;
text-decoration: none;
}
.extlink {
color: black;
text-decoration: none;
}
.jourlink {
color: black;
text-decoration: none;
}
#topbar {
display: inline-block;
padding: 0 0.25em;
}
div#annoucement {
width: 45em;
}
table#table1 {
text-align: left;
margin-left: 35;
margin-right: auto;
}
ul#course {
list-style: none;
padding-left: 5;
}
.links {
display: none;
}
/* The navigation bar */
.navbar {
display: none;
opacity: 0.8;
overflow: hidden;
background-color: #3c3836;
position: fixed;
/* Set the navbar to fixed position */
top: 0;
/* Position the navbar at the top of the page */
left: 0;
width: 100%;
/* Full width */
text-align: center;
font-weight: bold;
-webkit-text-size-adjust: 150%;
}
/* Links inside the navbar */
.navbar a {
/* float: left; */
color: white;
}
hr {
border-top: dashed 0.1em;
}
.notATable {
display: table;
list-style: none;
padding-left: 5;
-webkit-text-size-adjust: 120%;
/* font-size:16px; */
}
.notATable>li {
display: table-row;
}
.notATable>li>* {
display: table-cell;
padding: 0.125em;
}
.notATable label {
font-weight: bold;
text-align: right;
}
.notATable label:after {
content: '|';
}
#shadowbox {
border: 0em solid;
border-radius: 1em;
padding: 0.6em;
box-shadow: 0.3em 0.3em 1em #7c6f64;
}
hr.style-one {
display: none;
border: 0;
height: 0.1em;
background: #282828;
background-image: -webkit-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -moz-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -ms-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -o-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
}
hr.style-zero {
display: none;
border: 0;
height: 0em;
background: #282828;
background-image: -webkit-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -moz-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -ms-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -o-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
}
hr.curve {
border: 0;
height: 1em;
background-image: url(curve.png);
background-size: 100% 100%;
background-repeat: no-repeat;
}
.box {
width: 100%;
height: 18em;
background: rgb(220, 220, 220);
margin: 2.5em auto;
}
.effect2 {
position: relative;
}
.effect2:before,
.effect2:after {
z-index: -1;
position: absolute;
content: "";
bottom: 1em;
left: 0.5em;
width: 50%;
top: 80%;
max-width: 18empx;
background: #777;
-webkit-box-shadow: 0 1em 0.5em #777;
-moz-box-shadow: 0 1em 0.5em #777;
box-shadow: 0 1em 0.5em #777;
-webkit-transform: rotate(-3deg);
-moz-transform: rotate(-3deg);
-o-transform: rotate(-3deg);
-ms-transform: rotate(-3deg);
transform: rotate(-3deg);
}
.effect2:after {
-webkit-transform: rotate(3deg);
-moz-transform: rotate(3deg);
-o-transform: rotate(3deg);
-ms-transform: rotate(3deg);
transform: rotate(3deg);
right: 0.5em;
left: auto;
}
.container {
display: none;
}
#container_rotate {
-webkit-transform: rotate(90deg);
-moz-transform: rotate(90deg);
-o-transform: rotate(90deg);
-ms-transform: rotate(90deg);
transform: rotate(90deg);
}
.ball {
width: 0.0em;
height: 0.0em;
margin: 0.0em auto;
border-radius: 0em;
background: white;
}
/* Dark Mode */
.dark-mode a {
color: #83a598;
}
.dark_mode_authorlink {
color: #83a598;
}
.dark_mode_paperlink {
color: #fb4934;
}
.dark_mode_extlink {
color: #8ec07c;
}
.dark_mode_jourlink {
color: #8ec07c;
}
.dark_mode_body {
background-color: white;
color: black;
font-weight: 500;
}
.dark_mode_navbar {
background-color: #ebdbb2;
}
.dark_mode_navbar_a {
color: #f2f2f2;
}
.dark_mode_navbar_a_hover {
background: #3c3836;
color: #f9f5d7;
}
.dark_mode_ball {
background: #fbf1c7;
}
.dark_mode_style-one {
border: 0;
height: 0.1em;
background: #f9f5d7;
background-image: -webkit-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -moz-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -ms-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -o-linear-gradient(left, #282828, #f9f5d7, #282828);
}
.dark_mode_style-zero {
border: 0;
height: 0em;
background: #f9f5d7;
background-image: -webkit-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -moz-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -ms-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -o-linear-gradient(left, #282828, #f9f5d7, #282828);
}
#blackboard {
display: none;
}

458
style.css
View File

@@ -1,182 +1,464 @@
html {
scroll-behavior: smooth;
max-width: 800px;
margin: auto;
scroll-behavior: smooth;
max-width: 50em;
margin: auto;
}
body {
font-family: "Palatino", "Georgia", Times, serif;
background-color: rgb(255, 255, 250);
line-height: 1.4;
padding-bottom: 200px;
font-family: "Georgia", Times, serif;
background-color: #f9f5d7;
color: #282828;
line-height: 1.4;
font-weight: 500;
padding-bottom: 12.5em;
}
img {
border-radius: 15px;
border-radius: 1em;
}
h1, h2, h3, h4 {
padding-top: 0px;
padding-bottom: 10px;
text-align: center;
h1,
h2,
h3,
h4 {
padding-top: 0em;
padding-bottom: 0.5em;
text-align: center;
}
th{
font-weight: normal;
th {
font-weight: normal;
}
p {
padding-bottom: 10px;
padding-bottom: 0.5em;
}
#topbar{
a {
color: #076678;
}
.authorlink {
color: #076678;
text-decoration: none;
}
.paperlink {
font-family: "Georgia", Times, serif;
color: #9d0006;
text-decoration: none;
}
.extlink {
color: #427b58;
}
.jourlink {
color: #427b58;
text-decoration: none;
}
#topbar {
display: inline-block;
padding: 0 5px;
padding: 0 0.25em;
}
div#annoucement {
width: 750px;
width: 45em;
}
table#table1 {
text-align:left;
margin-left:35;
margin-right:auto;
text-align: left;
margin-left: 35;
margin-right: auto;
}
ul#course {
list-style: none;
padding-left: 5;
list-style: none;
padding-left: 5;
}
/* The navigation bar */
.navbar {
opacity: 0.8;
overflow: hidden;
background-color: #333;
position: fixed; /* Set the navbar to fixed position */
top: 0; /* Position the navbar at the top of the page */
left: 0;
width: 100%; /* Full width */
text-align: center;
font-weight: bold;
backdrop-filter: blur(3px);
overflow: hidden;
background-color: #3c3836AA;
position: fixed;
/* Set the navbar to fixed position */
top: 0;
/* Position the navbar at the top of the page */
left: 0;
width: 100%;
/* Full width */
text-align: center;
font-family: "Optima", "Georgia", Times, serif;
font-weight: bold;
-webkit-text-size-adjust: 150%;
}
/* Links inside the navbar */
.navbar a {
/* float: left; */
display: inline-block;
color: #f2f2f2;
text-align: center;
padding: 10px 16px;
text-decoration: none;
/* float: left; */
display: inline-block;
color: #f9f5d7;
text-align: center;
padding: 0.625em 1em;
text-decoration: none;
}
/* Change background on mouse-over */
.navbar a:hover {
background: #ddd;
color: black;
background: #f9f5d7;
color: #3c3836;
}
/* Main content */
.main {
margin-top: 5px; /* Add a top margin to avoid content overlay */
margin-top: 0.3em;
/* Add a top margin to avoid content overlay */
}
hr {
border-top: dashed 1px;
border-top: dashed 0.1em;
}
.notATable {
display:table;
list-style:none;
padding-left:5;
display: table;
list-style: none;
padding-left: 5;
-webkit-text-size-adjust: 120%;
/* font-size:16px; */
}
.notATable > li
{
display:table-row;
.notATable>li {
display: table-row;
}
.notATable > li > *
{
display:table-cell;
padding:2px;
.notATable>li>* {
display: table-cell;
padding: 0.125em;
}
.notATable label {
font-weight:bold;
text-align:right;
font-weight: bold;
text-align: right;
}
.notATable label:after {
content: '|';
content: '|';
}
#shadowbox {
border: 0px solid;
border-radius: 15px;
padding: 10px;
box-shadow: 5px 5px 18px #999999;
border: 0em solid;
border-radius: 1em;
padding: 0.6em;
box-shadow: 0.3em 0.3em 1em #7c6f64;
}
hr.style-one {
border: 0;
height: 1px;
background: #333;
background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc);
background-image: -moz-linear-gradient(left, #ccc, #333, #ccc);
background-image: -ms-linear-gradient(left, #ccc, #333, #ccc);
background-image: -o-linear-gradient(left, #ccc, #333, #ccc);
border: 0;
height: 0.1em;
scroll-margin-top: 2.5em;
background: #282828;
background-image: -webkit-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -moz-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -ms-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -o-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
}
hr.style-zero {
border: 0;
height: 0em;
background: #282828;
background-image: -webkit-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -moz-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -ms-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
background-image: -o-linear-gradient(left, #f9f5d7, #282828, #f9f5d7);
}
hr.curve {
border: 0;
height: 15px;
background-image: url(curve.png);
background-size: 100% 100%;
background-repeat: no-repeat;
border: 0;
height: 1em;
background-image: url(curve.png);
background-size: 100% 100%;
background-repeat: no-repeat;
}
.box {
width:100%;
height:280px;
background:rgb(220, 220, 220);
margin:40px auto;
width: 100%;
height: 18em;
background: rgb(220, 220, 220);
margin: 2.5em auto;
}
.effect2
{
.effect2 {
position: relative;
}
.effect2:before, .effect2:after
{
.effect2:before,
.effect2:after {
z-index: -1;
position: absolute;
content: "";
bottom: 15px;
left: 10px;
bottom: 1em;
left: 0.5em;
width: 50%;
top: 80%;
max-width:300px;
max-width: 18empx;
background: #777;
-webkit-box-shadow: 0 15px 10px #777;
-moz-box-shadow: 0 15px 10px #777;
box-shadow: 0 15px 10px #777;
-webkit-box-shadow: 0 1em 0.5em #777;
-moz-box-shadow: 0 1em 0.5em #777;
box-shadow: 0 1em 0.5em #777;
-webkit-transform: rotate(-3deg);
-moz-transform: rotate(-3deg);
-o-transform: rotate(-3deg);
-ms-transform: rotate(-3deg);
transform: rotate(-3deg);
}
.effect2:after
{
.effect2:after {
-webkit-transform: rotate(3deg);
-moz-transform: rotate(3deg);
-o-transform: rotate(3deg);
-ms-transform: rotate(3deg);
transform: rotate(3deg);
right: 10px;
right: 0.5em;
left: auto;
}
.container {
width: 12.5em;
height: 12.5em;
padding-top: 0em;
margin: 0 auto;
-webkit-transform: rotate(90deg);
-moz-transform: rotate(90deg);
-o-transform: rotate(90deg);
-ms-transform: rotate(90deg);
transform: rotate(90deg);
}
#container_rotate {
-webkit-transform: rotate(90deg);
-moz-transform: rotate(90deg);
-o-transform: rotate(90deg);
-ms-transform: rotate(90deg);
transform: rotate(90deg);
}
.ball {
width: 0.5em;
height: 0.5em;
margin: 0.5em auto;
border-radius: 3em;
background: #282828;
}
.ball:nth-child(1) {
-webkit-animation: right 1s infinite ease-in-out;
-moz-animation: right 1s infinite ease-in-out;
animation: right 1s infinite ease-in-out;
}
.ball:nth-child(2) {
-webkit-animation: left 1.1s infinite ease-in-out;
-moz-animation: left 1.1s infinite ease-in-out;
animation: left 1.1s infinite ease-in-out;
}
.ball:nth-child(3) {
-webkit-animation: right 1.05s infinite ease-in-out;
-moz-animation: right 1.05s infinite ease-in-out;
animation: right 1.05s infinite ease-in-out;
}
.ball:nth-child(4) {
-webkit-animation: left 1.15s infinite ease-in-out;
-moz-animation: left 1.15s infinite ease-in-out;
animation: left 1.15s infinite ease-in-out;
}
.ball:nth-child(5) {
-webkit-animation: right 1.1s infinite ease-in-out;
-moz-animation: right 1.1s infinite ease-in-out;
animation: right 1.1s infinite ease-in-out;
}
.ball:nth-child(6) {
-webkit-animation: left 1.05s infinite ease-in-out;
-moz-animation: left 1.05s infinite ease-in-out;
animation: left 1.05s infinite ease-in-out;
}
.ball:nth-child(7) {
-webkit-animation: right 1s infinite ease-in-out;
-moz-animation: right 1s infinite ease-in-out;
animation: right 1s infinite ease-in-out;
}
@-webkit-keyframes right {
0% {
-webkit-transform: translate(-1em);
}
50% {
-webkit-transform: translate(1em);
}
100% {
-webkit-transform: translate(-1em);
}
}
@-webkit-keyframes left {
0% {
-webkit-transform: translate(1em);
}
50% {
-webkit-transform: translate(-1em);
}
100% {
-webkit-transform: translate(1em);
}
}
@-moz-keyframes right {
0% {
-moz-transform: translate(-1em);
}
50% {
-moz-transform: translate(1em);
}
100% {
-moz-transform: translate(-1em);
}
}
@-moz-keyframes left {
0% {
-moz-transform: translate(1em);
}
50% {
-moz-transform: translate(-1em);
}
100% {
-moz-transform: translate(1em);
}
}
@keyframes right {
0% {
transform: translate(-1em);
}
50% {
transform: translate(1em);
}
100% {
transform: translate(-1em);
}
}
@keyframes left {
0% {
transform: translate(1em);
}
50% {
transform: translate(-1em);
}
100% {
transform: translate(1em);
}
}
/* Dark Mode */
.dark-mode a {
color: #83a598;
}
.dark_mode_authorlink {
color: #83a598;
}
.dark_mode_paperlink {
color: #fb4934;
}
.dark_mode_extlink {
color: #8ec07c;
}
.dark_mode_jourlink {
color: #8ec07c;
}
.dark_mode_body {
background-color: #1d2021;
color: #fbf1c7;
font-weight: 500;
}
.dark_mode_navbar {
background-color: #ebdbb2;
}
.dark_mode_navbar_a {
color: #f2f2f2;
}
.dark_mode_navbar_a_hover {
background: #3c3836;
color: #f9f5d7;
}
.dark_mode_ball {
background: #fbf1c7;
}
.dark_mode_style-one {
border: 0;
height: 0.1em;
background: #f9f5d7;
background-image: -webkit-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -moz-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -ms-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -o-linear-gradient(left, #282828, #f9f5d7, #282828);
}
.dark_mode_style-zero {
border: 0;
height: 0em;
background: #f9f5d7;
background-image: -webkit-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -moz-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -ms-linear-gradient(left, #282828, #f9f5d7, #282828);
background-image: -o-linear-gradient(left, #282828, #f9f5d7, #282828);
}
.fade-in {
opacity: 1;
animation-name: fadeInOpacity;
animation-iteration-count: 1;
animation-timing-function: ease-in;
animation-duration: 0.3s;
}
@keyframes fadeInOpacity {
0% {
opacity: 0;
}
100% {
opacity: 1;
}
}