具有状态切换的二人零和随机微分对策的动态规划原理
Dynamic Programming Principles for Two-Player Zero-Sum Stochastic Differential Games with Regime Switching
摘要: 本文研究了具有状态切换的二人零和随机微分对策,主要结果是在倒向随机微分方程框架下具有状态切换的二人零和随机微分对策的动态规划原理。
Abstract: In this paper, we study dynamic programming principles for two-player zero-sum stochastic dif-ferential games with regime switching. The main results of this paper concern dynamic program-ming principles with the help of the theory of backward stochastic differential equations.
文章引用:李钧瑶. 具有状态切换的二人零和随机微分对策的动态规划原理[J]. 理论数学, 2021, 11(4): 654-662. https://doi.org/10.12677/PM.2021.114079

参考文献

[1] Fleming, W.H. and Souganidis, P.E. (1989) On the Existence of Value Functions of Two-Player, Zero-Sum Stochastic Differential Games. Indiana University Mathematics Journal, 38, 293-314.
[2] Buckdahn, R. and Li, J. (2008) Stochastic Differential Games and Viscosity Solutions of Hamilton-Jacobi-Bellman-Isaacs Equations. SIAM Journal on Control & Optimization, 47, 444-475. [Google Scholar] [CrossRef
[3] Fleming, W.H. and Soner, H.M. (2006) Controlled Markov Processes and Viscosity Solutions. Springer, New York.
[4] Jiong, M.Y. and Zhou, X.Y. (1999) Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer Verlag, Berlin.
[5] Buckdahn, R., Cardaliaguet, P. and Quincampoix, M. (2011) Some Recent Aspects of Differential Game Theory. Dynamic Games & Applications, 1, 74-114. [Google Scholar] [CrossRef