On Zero-Sum Stochastic Differential Games with Jump-Diffusion Driven State: A Viscosity Solution Framework

Abstract

A zero-sum differential game with controlled jump-diffusion driven state is considered and studied by a combination of dynamic programming and viscosity solution techniques. We prove, under certain conditions, that the value of the game exists. Moreover, the value function is shown to be the unique viscosity solution of a fully nonlinear integro-partial differential equation. In addition, we formulate and prove a verification theorem for such games within the viscosity solution framework for nonlocal equations.