On the value of stochastic differential games

Wendell H. Fleming · Daniel Hernández–Hernández

38 citations0/0 files storedCommunications on Stochastic Analysis

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Game Theory and Applications

Abstract

We consider a two player, zero sum stochastic differential game based on a formulation given by Fleming and Souganidis.The saddle point property is introduced, and it is proved that the unique uniformly continuous bounded viscosity solution of the upper Isaacs PDE with boundary condition satisfies such a property.Also, it is shown that approximately optimal Markov strategies can be constructed for both players.

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References

2005Controlled Markov Processes and Viscosity Solutions 2007Stochastic Differential Games and Viscosity Solutions of Hamilton-Jacobi-Bellman-Isaacs Equations

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2016Zero-sum risk-sensitive stochastic games 2013Zero-sum risk-sensitive stochastic games on a countable state space 2020Zero-sum path-dependent stochastic differential games in weak formulation 2013Linear-Quadratic Stochastic Differential Games with General Noise Processes

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