Two-player zero-sum stochastic differential games with Markov-switching jump-diffusion dynamics

Abstract

We consider a two-player zero-sum stochastic differential game (SDG) with hybrid state variable dynamics given by a Markov-switching jump-diffusion. We study this game using a combination of dynamic programming and viscosity solution techniques, generalizing the seminal work of Fleming and Souganidis to a broader class of SDGs. Under some mild assumptions, we prove that the value of the game exists and is the unique viscosity solution of a certain nonlinear partial integro-differential equation of Hamilton-Jacobi-Bellman-Isaacs type.