On Optimal Tracking Portfolio in Incomplete Markets: The Reinforcement Learning Approach, (with Y.J. Huang and X. Yu). To appear in SIAM Journal on Control and Optimization [arXiv]
Stochastic Control Problems with State-Reflections Arising From Relaxed Benchmark Tracking, (with Y.J. Huang and X. Yu). To appear in Mathematics of Operations Research [arXiv]
The Cooperative Mean Field Game for Production Control with Sticky Price, (with T.Q. Li). To appear in Communications in Mathematics and Statistics
Extended Mean Field Control Problems with Constraints: The Generalized Fritz-John Conditions and Lagrangian Method, (with J.F. Wang and X. Yu). [arXiv]: In the present paper, we study extended mean field control problems under both the dynamic expectation constraints and the dynamic state-control constraints from the perspective of optimization problems with Banach space valued constraints. We propose a new methodology that bridges the SMP method for the C-(E)MFC problems and the Lagrange multipliers method with the generalized Fritz-John (FJ) optimality condition. In a nutshell, when the forward McKean-Vlasov state process is taken as an infinite-dimensional constraints, the generalized FJ optimality condition for the control variable yields the stochastic (first-order) minimum condition that leads to the SMP. Meanwhile, the generalized Lagrangian multiplier in the space of Ito processes induced by the FJ optimality condition on the state variable gives us the adjoint process as the solution to the BSDE. As a result, formally, in the degenerate case, the Pontryagin's maximum principle is a KKT type optimality condition.
Selected Publications
(A full list of journal papers on Google Scholar is here)
A Mean Field Game Approach to Equilibrium Consumption under External Habit Formation, (with S.H. Wang and X. Yu). Stochastic Processes and their Applications Vol. 178, paper no. 104461, 2024.
A Mean Field Game Approach to Optimal Investment and Risk Control for Competitive Insurers, (with S.H. Wang and C. Zhou). Insurance: Mathematics and Economics Vol. 116, 202-217, 2024.
Mean Field Game of Optimal Relative Investment with Jump Risk, (with S.H. Wang and X. Yu). Science China Mathematics Vol. 67, 1159-1188, 2024. [arXiv]
Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors, (with A. Capponi and C. Zhou). Mathematics of Operations Research Vol. 48(1), 288-312, 2023.
Large Sample Mean-Field Stochastic Optimization, (with A. Capponi and H.F. Liao). [Previous Title: Deep Residual Learning via Large Sample Mean-Field Stochastic Optimization] SIAM Journal on Control and Optimization Vol. 60(4), 2538-2573, 2022. [arXiv]
Risk-sensitive Credit Portfolio Optimization under Partial Information and Contagion Risk, (with H.F. Liao and X. Yu). The Annals of Applied Probability Vol. 32(4), 2355-2399, 2022. [arXiv]
Probabilistic Analysis of Replicator-Mutator Equations, (with H.F. Liao). Advances in Applied Probability Vol. 54(1), 167-201, 2022.
Approximating Nash Equilibrium for Optimal Consumption in Stochastic Growth Model with Jumps, (with Q.T. Li). Acta Mathematica Sinica, English Series Vol. 38, 1621-1642, 2022.
Centralized Systemic Risk Control in the Interbank System: Weak Formulation and Gamma-Convergence, (with T.Q. Li and X. Yu). Stochastic Processes and their Applications Vol. 150(3), 622-654, 2022. [arXiv]
Dynamic Analysis of Counterparty Exposures and Netting Efficiency of Central Counterparty Clearing, (with Y.C. Liu and T.T. Zhang). Quantitative Finance Vol. 21(7), 1187-1206, 2021.
Locally Risk-Minimizing Hedging of Counterparty Risk for Portfolio of Credit Derivatives, (with C. Ceci). Applied Mathematics and Optimization Vol. 82, 799-850, 2020.
Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching, (with H.F. Liao and X. Yu). SIAM Journal on Control and Optimization Vol. 57(1), 366-401, 2019. [arXiv]
Optimal Credit Investment and Risk Control for An Insurer with Regime-Switching, (with H.F. Liao and Y.J. Wang). Mathematics and Financial Economics Vol. 13, 147-172, 2019.
Credit Portfolio Selection with Decaying Contagion Intensities, (with A. Capponi and P.C. Chen). Mathematical Finance Vol. 29(1), 137-173, 2019. [SSRN]
Optimal Investment of Variance-Swaps in Jump-Diffusion Market with Regime-Switching, (with D. Tang and Y.J. Wang). Journal of Economic Dynamics and Control Vol. 83, 175-197, 2017.
Bilateral Credit Valuation Adjustment for Large Credit Derivatives Portfolios, (with A. Capponi). Finance and Stochastics Vol. 18(2), 431-482, 2014. [arXiv]
Smooth-pasting Property on Reflected Levy Processes and Its Applications in Credit Risk Modeling, (with X.W. Yang). Science China Mathematics Vol. 57, 1237-1256, 2014.
Kernel-Correlated Levy Field Driven Forward Rate and Application to Derivative Pricing, (with X.W. Yang). Applied Mathematics and Optimization Vol. 68(1), 21-41, 2013.
First Passage Times of Reflected O-U Processes with Two-Sided Jumps. Queueing Systems Vol. 73(1), 105-118, 2013.
Levy Risk Model with Two-Sided Jumps and A Barrier Dividend Strategy, (with R.M. Song, D. Tang and X.W. Yang). Insurance: Mathematics and Economics Vol. 50(2), 280-291, 2012.
Exponential Change of Measure Applied To Term Structures of Interest Rates and Exchange Rates. Insurance: Mathematics and Economics Vol. 49(2), 216-225, 2011.
On the First Passage Times of Reflected OU Processes with Two-Sided Barriers, (with Y. Wang and L. Zhang). Queueing Systems Vol. 54(4), 313-316, 2006.
Markov-Modulated Jump-Diffusions for Currency Option Pricing, (with Y. Wang and X. Yang). Insurance: Mathematics and Economics Vol. 46(3), 461-469, 2010.
An Optimal Portfolio Problem in a Defaultable Market, (with Y. Wang and X. Yang). Advances in Applied Probability Vol. 42(3), 689-705, 2010.
Support Theorem for a Stochastic Cahn-Hilliard Equation, (with K. Shi and Y. Wang). Electronic Journal of Probability Vol. 15(1), 484-525, 2010.
On a Stochastic Wave Equation Driven by a Non-Gaussian Levy Process, (with K. Shi and Y. Wang). Journal of Theoretical Probability Vol. 23(1), 328-343, 2010.
Explosive Solutions of Stochastic Wave Equations with Damping on R^d, (with D. Tang and Y. Wang). Journal of Differential Equations Vol. 244(1), 170-187, 2008.