Open Access
Volume 28, 2022
Article Number 25
Number of page(s) 21
Published online 26 May 2022
  1. R. Buckdahn and Y. Hu, Probabilistic interpretation of a coupled system of Hamilton-Jacobi-Bellman equations. J. Evol. Equ. 10 (2010) 529–549. [CrossRef] [MathSciNet] [Google Scholar]
  2. R. Buckdahn and J. Li, Stochastic differential games and viscosity solutions for Hamilton-Jacobi-Bellman-Isaacs equations. SIAM J. Control Optim. 47 (2008) 444–475. [Google Scholar]
  3. M.G. Crandall, H. Ishii and P.L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1–67. [Google Scholar]
  4. L. Denis, M. Hu and S. Peng, Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths. Potential Anal. 34 (2011) 139–161. [Google Scholar]
  5. L. Denis and C. Martini, A theoretical framework for the pricing of contingent claims in the presence of model uncertainty. Ann. Appl. Probab. 16 (2006) 827–852. [CrossRef] [MathSciNet] [Google Scholar]
  6. L. Denis and K. Kervarec, Optimal investment under model uncertainty in non-dominated models. SIAM J. Control Optim. 51 (2013) 1803–1822. [Google Scholar]
  7. N. El Karoui, S. Peng and M.C. Quenez, Backward stochastic differential equations in finance. Math. Finance 7 (1997) 1–71. [Google Scholar]
  8. L. Epstein and S. Ji, Ambiguous volatility, possibility and utility in continuous time. J. Math. Econom. 50 (2014) 269–282. [CrossRef] [MathSciNet] [Google Scholar]
  9. L. Epstein and S. Ji, Ambiguous volatility and asset pricing in continuous time. Rev. Financ. Stud. 26 (2013) 1740–1786. [Google Scholar]
  10. W.H. Fleming and H.M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer (1992). [Google Scholar]
  11. M. Hu and S. Ji, Dynamic programming principle for stochastic recursive optimal control problem driven by a G-Brownian motion. Stoch. Process. Appl. 127 (2017) 107–134. [Google Scholar]
  12. M. Hu, S. Ji, S. Peng and Y. Song, Backward stochastic differential equations driven by G-Brownian motion. Stochastic Process. Appl. 124 (2014) 759–784. [Google Scholar]
  13. M. Hu, S. Ji, S. Peng and Y. Song, Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion. Stochastic Process. Appl. 124 (2014) 1170–1195. [Google Scholar]
  14. M. Hu, S. Ji and X. Xue, The existence and uniqueness of viscosity solution to a kind of Hamilton-Jacobi-Bellman equation. SIAM J. Control Optim. 57 (2019) 3911–3938. [Google Scholar]
  15. M. Hu and S. Peng, On representation theorem of G-expectations and paths of G-Brownian motion. Acta Math. Appl. Sin. Engl. Ser. 25 (2009) 539–546. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Hu, F. Wang and G. Zheng, Quasi-continuous random variables and processes under theG-expectation framework. Stoch. Process. Appl. 126 (2016) 2367–2387. [Google Scholar]
  17. J. Li and Q. Wei, Optimal control problems of fully coupled FBSDEs and viscosity solutions of Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 52 (2014) 1622–1662. [Google Scholar]
  18. A. Matoussi, D. Possamai and C. Zhou, Robust Utility maximization in non-dominated models with 2BSDEs. Math. Finance 25 (2015) 258–287. [CrossRef] [MathSciNet] [Google Scholar]
  19. J. Ma, P. Protter and J. Yong, Solving forward-backward stochastic differential equations explicitly - a four step scheme. Probab. Theory Related Fields 98 (1994) 339–359. [Google Scholar]
  20. J. Ma and J. Yong, Forward-Backward Stochastic Differential Equations and Their Applications, Lect. Notes Math. Springer (1999). [Google Scholar]
  21. S. Peng, Nonlinear expectations and nonlinear Markov chains. Chin. Ann. Math. 26B (2005) 159–184. [CrossRef] [Google Scholar]
  22. S. Peng, G-expectation, G-Brownian Motion and Related Stochastic Calculus of Ito type. Stochastic analysis and applications, Abel Symp., Vol. 2, Springer, Berlin (2007) 541–567. [Google Scholar]
  23. S. Peng, Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stochastic Process. Appl. 118 (2008) 2223–2253. [Google Scholar]
  24. S. Peng, A generalized dynamic programming principle and Hamilton-Jacobi-Bellmen equation. Stoch. Stoch. Rep. 38 (1992) 119–134. [Google Scholar]
  25. S. Peng, Backward stochastic differential equations—stochastic optimization theory and viscosity solutions of HJB equations, in Topics on Stochastic Analysis, edited by J. Yan, S. Peng, S. Fang, and L. Wu. Science Press, Beijing (1997) 85–138 (in Chinese). [Google Scholar]
  26. S. Peng, Nonlinear Expectations and Stochastic Calculus under Uncertainty. Springer (2019). [CrossRef] [Google Scholar]
  27. T. Pham and J. Zhang, Two person zero-sum game in weak formulation and path dependent Bellman-Isaacs equation. SIAM J. Control Optim. 52 (2014) 2090–2121. [Google Scholar]
  28. H.M. Soner, N. Touzi and J. Zhang, Wellposedness of second order backward SDEs. Probab. Theory Related Fields 153 (2012) 149–190. [Google Scholar]
  29. S. Tang, Dynamic programming for general linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 53 (2015) 1082–1106. [Google Scholar]
  30. Z. Wu and Z. Yu, Probabilistic interpretation for a system of quasilinear parabolic partial differential equation combined with algebra equations. Stochastic Process. Appl. 124 (2014) 3921–3947. [Google Scholar]
  31. J. Yong and X.Y. Zhou, Stochastic controls: Hamiltonian systems and HJB equations. Springer (1999). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.