On zero-sum Stochastic Differential Games with Jump-Diffusion driven state: A viscosity solution framework

Details On zero-sum Stochastic Differential Games with Jump-Diffusion driven state: A viscosity solution framework On zero-sum Stochastic Differential Games with Jump-Diffusion driven state: A viscosity solution framework

2010-09-24

arxiv.org/abs/1009.4949v1

Mathematics

Optimization and Control

Siam Journal of Control and Optimization (second revision submitted)

Scientific paper

A zero-sum differential game with controlled jump-diffusion driven state is considered, and studied using a combination of dynamic programming and viscosity solution techniques. We prove, under certain conditions, that the value of the game exists and is 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

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