Stochastic Control; Market Frictions; Market Microstructure; FinTech; Deep Learning for Stochastic Control.
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Publications
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Selected Publications
Optimal Investment under Block-Shaped Order Books (with Nan Chen, Min Dai, and Qiheng Ding).
working paper.
@@ -88,8 +96,9 @@ Stochastic Control; Market Frictions; Market Microstructure; FinTech; Deep Learn
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.
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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.
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A Stochastic Representation for Nonlocal Parabolic PDEs with Applications (with Min Dai and Steven Kou).
- Mathematics of Operations Research, forthcoming. [Abstract|SSRN|Article]
+ Mathematics of Operations Research, 47(3):1707-2545, 2022 [Abstract|SSRN|Article]
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.
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