Research

My research interests are mainly focused on mathematical finance and stochastic control.  I am especially interested in 

1. stochastic control and backward stochastic differential equations; 

2. optimal stopping and free boundary problems; 

3. viscosity solutions and numerics; 

4. optimal investment and forward preferences; 

5. credit and funding liquidity risks.

Publications: 

1. Recursive optimal stopping with Poisson stopping constraints (with Wei Wei, Zhen Wu and Zhenda Xu), SIAM Journal on Control and Optimization, Vol. 63, No. 4,  (2025), 2734--2762. [arXiv] [PDF].

2. Convergence rates for Chernoff-type approximations of convex monotone semigroups (with Jonas Blessing, Lianzi Jiang, Michael Kupper),  Stochastic Processes and their Applications, Vol. 189, (2025), 104700, 1--28. [arXiv] [PDF].

3. Ergodic singular stochastic control motivated by the optimal sustainable exploitation of an ecosystem, (with Zhesheng Liu and Mihail Zervos), SIAM Journal on Control and Optimization,  Vol. 63, No. 3,  (2025), 2029--2052. [arXiv] [PDF]. 

4. On the rate of convergence for an α-stable central limit theorem under sublinear expectation, (with Mingshang Hu and Lianzi Jiang), Journal of Applied Probability, Vol. 62, No. 1, (2025), 209-233. [arXiv] [PDF]

5. Callable convertible bonds under liquidity constraints and hybrid priorities, (with David Hobson and Edward Wang), SIAM Journal on Financial Mathematics, Vol. 15, No. 4,  (2024), 1083--1123. [arXiv] [PDF]

6. A robust α-stable central limit theorem under sublinear expectation without integrability condition,  (with Lianzi Jiang), Journal of Theoretical Probability, Vol.37, (2024), 2394-2424, [arXiv] [PDF] 

7. A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem, (with Shuo Huang), Journal of Differential Equations, Vol.398, (2024), 1-37, [arXiv] [PDF]

8. Introduction for recent advances in forward performance processes (with Thaleia Zariphopoulou), Probability, Uncertainty, and Quantitative Risk, Vol. 9, No. 2, (2024), i-iii. [PDF] 

9. Optimal investment and consumption with forward preferences and uncertain parameters, (with Wing Fung Alfred Chong),  Probability, Uncertainty and Quantitative Risk,  Vol.9, No.1, (2024), 65-84. [arXiv] [PDF]

10. Predictable forward performance processes: Infrequent evaluation and applications to human-machine interactions, (with Moris Strub and Yuwei Wang),  Mathematical Finance,  Vol.33, No.4, (2023), 1248-1286. [arXiv] [PDF]

11. A new monotonicity condition for ergodic BSDEs and ergodic control with super-quadratic Hamiltonians, (with Joe Jackson), SIAM Journal on Control and Optimization, Vol.61, No.3, (2023), 1273-1296. [arXiv] [PDF]  

12. A universal robust limit theorem for nonlinear Levy processes under sublinear expectation, (with Mingshang Hu, Lianzi Jiang and Shige Peng), Probability, Uncertainty and Quantitative Risk, Vol.8, No.1, (2023), 1-32. [arXiv] [PDF]  

13. Quantitative stability and numerical analysis of Markovian quadratic BSDEs with reflection, (with Dingqian Sun and Shanjian Tang), Probability, Uncertainty and Quantitative Risk, Vol.7, No.1, (2022), 13-30. [arXiv] [PDF]

14. A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models, (with Juan Li and Wenqiang Li),  SIAM Journal on Financial Mathematics, Vol.12, No.3, (2021), 867-897. [arXiv] [PDF]

15. Analysis of the optimal exercise boundary of American put option with delivery lags, (with Zhou Yang), Journal of Mathematical Analysis and Application,  Vol.497, No.2, (2021), 124916, 1-21. [arXiv] [PDF]

16. Pricing vulnerable options in a hybrid credit risk model driven by Heston-Nandi GARCH processes, (with Xingchun Wang), Review of Derivatives Research, Vol.24, No.1, (2021), 1-30. [arXiv] [PDF]

17. Systems of ergodic BSDE arising in regime switching forward performance processes,  (with Ying Hu and Shanjian Tang), SIAM Journal on Control and Optimization, Vol.58, No.4, (2020), 2503-2534. [arXiv] [PDF]

18. An approximation scheme for semilinear parabolic PDEs with convex and coercive Hamiltonians, (with Shuo Huang and Thaleia Zariphopoulou), SIAM Journal on Control and Optimization,  Vol.58, No.1, (2020), 165–191. [arXiv] [PDF] 

19. Dynkin games with Poisson random intervention times, (with Haodong Sun), SIAM Journal on Control and Optimization, Vol.57, No. 4, (2019), 2962-–2991. [arXiv] [PDF]

20. An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior, (with Wing Fung Alfred Chong, Ying Hu and Thaleia Zariphopoulou), Finance and Stochastics, Vol.23, No.1, (2019), 239--273. [arXiv] [PDF]

21. Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs, (with Zhou Yang and Chao Zhou), Mathematics and Financial Economics, Vol.13, No.3, (2019), 393--427. [arXiv] [PDF]

22. Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE, (with Thaleia Zariphopoulou), SIAM Journal on Financial Mathematics, Vol.8, No.1, (2017), 344--372. [arXiv] [PDF]

23. A multidimensional exponential utility indifference pricing model with applications to counterparty risk, (with Vicky Henderson), SIAM Journal on Control and Optimization, Vol.54, No.2, (2016), 690--717. [arXiv] [PDF]

24. Optimal switching at Poisson random intervention times, (with Wei Wei), Discrete and Continuous Dynamical Systems-Series B, Vol.21, No.5, (2016), 1483--1505. [arXiv] [PDF]

25. Stochastic control representations for penalized backward stochastic differential equations, SIAM Journal on Control and Optimization, Vol.53, No.3, (2015), 1440--1463. [arXiv] [PDF]

26. Funding liquidity, debt tenor structure, and creditor's belief: An exogenous dynamic debt run model, (with Eva Lutkebohmert and Wei Wei), Mathematics and Financial Economics, Vol.9, No.4, (2015), 271--302. [arXiv] [PDF]

27. Dynkin game of convertible bonds and their optimal strategy, (with Huiwen Yan, Zhou Yang and Fahuai Yi), Journal of Mathematical Analysis and Application, Vol.426, No.1, (2015), 64--88. [arXiv] [PDF]

28. Indifference pricing and hedging in a multiple-priors model with trading constraints, (with Huiwen Yan and Zhou Yang), Science China Mathematics, Vol.58, No.4, (2015), 689--714. [arXiv] [PDF]

29. Fully coupled forward-backward stochastic dynamics and functional differential systems, (with Matteo Casserini), Stochastics and Dynamics, Vol.15, No.2, (2015), 1550006, 1--25. [arXiv] [PDF]

30. Pseudo linear pricing rule for utility indifference valuation, (with Vicky Henderson), Finance and Stochastics, Vol.18, No.3, (2014), 593--615. [arXiv] [PDF]

31. A multi-period bank run model for liquidity risk, (with Eva Lutkebohmert and Yajun Xiao), Review of Finance, Vol.18, No.2, (2014), 803--842. [SSRN] [PDF] [Appendix]

32. A modified structural model for credit risk, (with Lishang Jiang), IMA Journal of Management Mathematics, Vol.23, No.2, (2012), 147--170. [SSRN] [PDF]

33. The backward stochastic dynamics on a filtered probability space, (with Terry Lyons and Zhongmin Qian), Annals of Probability, Vol.39, No.4, (2011), 1422--1448. [arXiv] [PDF]

34. A functional approach to backward stochastic dynamics, DPhil thesis, University of Oxford, (2011). [PDF]

35. The valuation of the basket CDSs in a primary-subsidiary model, (with Jianwei Lin, Sen Wu and Harry Zheng), Asia-Pacific Journal of Operational Research, Vol.28, No.2, (2011), 213--238. [PDF]

36. The credit risk and pricing of OTC options, (with Xuemin Ren), Asia-Pacific Financial Markets, Vol.14, No.1, (2007), 45--68. [PDF]

Working Papers:

1. Probabilistic approximation of fully nonlinear second-order PIDEs with convergence rates for the universal robust limit theorem, (with Lianzi Jiang and Mingshang Hu),  arXiv:2506.18374. 

2. Zero-sum Dynkin games under common and independent Poisson constraints, (with David Hobson and Edward Wang), arXiv: 2411.07134. 

3. Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach (with Wing Fung Alfred Chong),  arXiv:2410.01378.

4. Representation of forward performance criteria with random endowment via FBSDE and application to forward optimized certainty equivalent (with Yifan Sun and Thaleia Zariphopoulou),  arXiv:2401.00103.

5. Predictable relative forward performance processes: Multi-agent and mean field games for portfolio management (with Moris Strub and Yuwei Wang),  arXiv:2311.04841.

6. Vague and weak convergence of signed measures  (with Martin Herdegen and Osian Shelley), arXiv:2205.13207.

7. A Tauberian Theorem for signed measures (with Martin Herdegen and Osian Shelley), arXiv:2205.13075.

8. Risk-sensitive Dynkin games with heterogeneous Poisson random intervention times, (with Haodong Sun), arXiv:2008.01787. 

9. Utility maximization in constrained and unbounded financial markets: Applications to indifference valuation, regime switching, consumption and Epstein-Zin recursive utility, (with Ying Hu and Shanjian Tang), arXiv:1707.00199. 

10. A functional approach to FBSDEs and its application in optimal portfolios, (with Terry Lyons and Zhongmin Qian), arXiv:1011.4499.