scholarly journals A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls

2013 ◽  
Vol 51 (3) ◽  
pp. 2036-2080 ◽  
Author(s):  
Erhan Bayraktar ◽  
Song Yao
Keyword(s):  
Dynamic Programming ◽  
Differential Games ◽  
Stochastic Differential Games ◽  
Dynamic Programming Principle ◽  
Unbounded Controls ◽  
Zero Sum

scholarly journals A BSDE Approach to Stochastic Differential Games with Regime Switching

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
J. Y. Li ◽  
M. N. Tang
Keyword(s):  
Dynamic Programming ◽  
Regime Switching ◽  
Time Horizon ◽  
Backward Stochastic Differential Equation ◽  
Stochastic Differential Games ◽  
Dynamic Programming Principle ◽  
Value Functions ◽  
Finite Time Horizon ◽  
Hamilton Jacobi Bellman ◽  
Zero Sum

In this paper, we study a two-player zero-sum stochastic differential game with regime switching in the framework of forward-backward stochastic differential equations on a finite time horizon. By means of backward stochastic differential equation methods, in particular that of the notion from stochastic backward semigroups, we prove a dynamic programming principle for both the upper and the lower value functions of the game. Based on the dynamic programming principle, the upper and the lower value functions are shown to be the unique viscosity solutions of the associated upper and lower Hamilton–Jacobi–Bellman–Isaacs equations.

Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games

2011 ◽  
Vol 153 (3) ◽  
pp. 662-687 ◽  
Author(s):  
Beatris Escobedo-Trujillo ◽  
Daniel López-Barrientos ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Differential Games ◽  
Stochastic Differential Games ◽  
Zero Sum
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