Publications

Animation for SelectNet method (Gu, Yang and Zhou JCP 2021)

Animation for SelectNet method:

Left: Green: SelectNet; Red: residual; Blue: solution error

Right: Red: residual v.s. iterations; Blue: solution error v.s. iterations

  1. Second order BSDEs with quadratic growth, with Possamaï, D., Stochastic Processes and their Applications, 2013, 123(10):3770-3799.

  2. Second order reflected backward stochastic differential equations, with Matoussi, A., Possamaï, D., The Annals of Applied Probability, 2015, 23(6):2420-2457.

  3. Robust utility maximization in non-dominated models with 2BSDEs, with Matoussi, A., Possamaï, D., Mathematical Finance, 2015, 25(2):258-287.

  4. Second order backward stochastic differential equations with jumps: formulation and uniqueness, with Kazi-Tani, N., Possamaï, D., The Annals of Applied Probability, 2015, 25(5)2867-2908.

  5. Second order BSDEs with jumps: existence and probabilistic representation for fully-nonlinear PIDEs, with Kazi-Tani, N., Possamaï, D., Electronic Journal of Probability, 2015, 20(65):1-31.

  6. The obstacle problem for semilinear parabolic partial integro-differential equations, with Matoussi, A., Sabbagh, W., Stochastics and Dynamics, 2015, 15(01)-1550007.

  7. Quadratic BSDEs with jumps: a fixed point approach, with Kazi-Tani, N., Possamaï, D., Electronic Journal of Probability, 2015, 20(66):1-28.

  8. Quadratic BSDEs with jumps: related non-linear expectations, with Kazi-Tani, N., Possamaï, D., Stochastics and Dynamics, 2016, 16(4)-1650012.

  9. The sustainable Black-Scholes equations, with Armenti, Y., Crépey, S., In: Londoño J., Garrido J., Jeanblanc M. (eds) Actuarial Sciences and Quantitative Finance. ICASQF 2016. Springer Proceedings in Mathematics & Statistics, 2017, vol 214: 155-167.

  10. A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, with Bouchard, B., Possamaï, D., Tan, X., Annales de l’Institut Henri Poincare (B), 2018, 54(1):154-172.

  11. Stochastic control for a class of nonlinear kernels and applications, with Possamaï, D., Tan, X., The Annals of Probability, 2018, 46(1):551-603.

  12. Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs, with Yang, Z., Liang, G., Mathematics and Financial Economics, 2019, 13(3):393-427.

  13. Second order BSDE under monotonicity condition and liquidation problem under uncertainty, with Popier, A., The Annals of Applied Probability, 2019, 29(3):1685-1739.

  14. Second order stochastic target problems with generalized market impact, with B. Bouchard, G. Loeper and H. M. Soner, SIAM Journal on Control and Optimization, 2019, 57(6):4125-4149.

  15. Deep learning algorithm to solve portfolio management with proportional transaction cost, with W. Zhang, In CIFEr 2019 - IEEE Conference on Computational Intelligence for Financial Engineering and Economics, 2019, available online doi: 10.1109/CIFEr.2019.8759056.

  16. Bank monitoring incentives under moral hazard and adverse selection, with Hernández Santibáñez, N., Possamaï, D., Journal of Optimization Theory and Applications, 2020, 184(3):988-1035.

  17. A risk-sharing framework of bilateral contracts, with J. Lee, S. Sturm, SIAM Journal on Financial Mathematics, 2020, 11(2):385-410.

  18. Horizon-unbiased investment with ambiguity, with Q. Lin and X. Sun, Journal of Economic Dynamics and Control, 2020, 114, 103896, published online https://doi.org/10.1016/j.jedc.2020.103896

  19. On dynamic programming principle for stochastic control under expectation constraints, with Y. Chow and X. Yu, Journal of Optimization Theory and Applications, 2020, 185:803-818.

  20. Lifetime ruin problem under high-watermark fees and drift uncertainty, with J. Lee and X. Yu, Applied Mathematics and Optimization, 2021, 84:2743-2773.

  21. Binary funding impacts in derivative valuation, with J. Lee, Mathematical Finance, 2021, 31(1):242-278.

  22. Erratum for “Second-order reflected backward stochastic differential equations” and “Second-order BSDEs with general reflection and game options under uncertainty”, with Matoussi, A., Possamaï, D., 2021. arXiv:1706.08588. The Annals of Applied Probability, 2021, 31(3):1505-1522.

  23. Gambling for resurrection and the heat equation on a triangle, with S. Ankirchner, C. Blanchet-Scalliet, and N. Kazi-Tani, Applied Mathematics and Optimization, 2021, 83(3):3111-3136.

  24. The Alpha-Heston stochastic volatility model, with Y. Jiao, C. Ma, and S. Scotti, Mathematical Finance, 2021, 31:943–978.

  25. SelectNet: Self-paced learning for high-dimensional partial differential equations, with Y. Gu and H. Yang, Journal of Computational Physics, 2021, 441:110444.

  26. Portfolio liquidation under factor uncertainty, with U. Horst and X. Xia, 2021, arXiv:1909.00748. The Annals of Applied Probability, 2022, 32(1):80-123.

  27. Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach, with H. Pham and X. Wei, Mathematical Finance, 2022, 32(1):349-404.

  28. Numerical methods for mean field games based on Gaussian Processes and Fourier Features, with C. Mou and X. Yang, Journal of Computational Physics, 1 July 2022, 460:111188.

  29. Power forward performance in semimartingale markets with stochastic integrated factors, with L. Bo and A. Capponi, 2022, https://doi.org/10.1287/moor.2022.1262. Mathematics of Operations Research, published online.

  30. The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation, with Q. Du, Y. Gu and H. Yang, 2022, arXiv:2103.11488. SIAM Journal on Numerical Analysis, 60(4):2014-2045.

  31. Mean Field Portfolio Games, with G. Fu, 2022, arXiv:2106.06185. Finance & Stochastics, 27, 189-231.

  32. Backward Stochastic Differential Equations and Backward Stochastic Volterra Integral Equations with Anticipating Generators, with H. Wang and J. Yong, 2022, Probability, Uncertainty and Quantitative Risk, accepted.

  33. A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEs, with J.-F. Chassagneux, J. Chen and N. Frikha, 2022, arXiv:2102.12051. IMA Journal of Numerical Analysis, accepted.

  34. Linear-Quadratic Mean Field Games of Controls with Non-Monotone Data, with M. Li, C. Mou and Z. Wu, 2022, arXiv:2206.01732. Transactions of the American Mathematical Society (TAMS), accepted.

  35. Robust control problems of BSDEs coupled with value functions, with Z. Yang and J. Zhang, 2022, arXiv:2208.10735, SIAM Journal on Financial Mathematics, accepted.

Last updated on May 4, 2020