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@@ -80,13 +80,13 @@ Optimal investment under market frictions; Stochastic Control; FinTech; Market m
Stochastic Representation for Nonlocal Problems (with Min Dai and Steven Kou).
- Mathematics of Operations Research, forthcoming. [SSRN]
+ Mathematics of Operations Research, forthcoming. [SSRN]
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.
Inventory Management for High-Frequency Trading with Imperfect Competition (with Sebastian Herrmann, Johannes Muhle-Karbe and Dapeng Shang).
- SIAM Journal on Financial Mathematics, forthcoming. [SSRN|arXiv]
+ SIAM Journal on Financial Mathematics, 11(1):1-26, 2020. [SSRN|arXiv|Article]
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.