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

2. On the rate of convergence for an α-stable central limit theorem under sublinear expectation, (with Mingshang Hu and Lianzi Jiang), Advances in Applied Probability, accepted. [arXiv] [PDF]

3. A robust α-stable central limit theorem under sublinear expectation without integrability condition,  (with Lianzi Jiang), Journal of Theoretical Probability, accepted. [arXiv] [PDF] 

4. 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]

5. 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]

6. 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]

7. 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]  

8. 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]  

9. 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]

10. 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]

11. 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), 1-21. [arXiv] [PDF]

12. 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]

13. 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]

14. 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] 

15. 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]

16. 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]

17. 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]

18. 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]

19. 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]

20. 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]

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

22. 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]

23. 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]

24. 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]

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

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

27. 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]

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

29. 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]

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

31. 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]

32. 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. 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.

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

3. Convergence rates for Chernoff-type approximations of convex monotone semigroups (with Jonas Blessing, Lianzi Jiang, Michael Kupper),  arXiv:2310.09830.

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

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

6. Callable convertible bonds under liquidity constraints and hybrid priorities, (with David Hobson and Edward Wang), arXiv:2111.02554. 

7. Ergodic singular stochastic control motivated by the optimal sustainable exploitation of an ecosystem, (with Mihail Zervos), arXiv:2008.05576. 

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.