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

2010/09/24 by Imran H. Biswas, Biswas, Imran H.
Economics, Econometrics and Finance · Engineering · Mathematics · #45K05 #46S50 #49L20 #49L25 #91A23 #93E20 #Analysis of PDEs (math.AP) #Economic theories and models #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1009.4949

openalex publication_date 2010/09/24 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

A zero-sum differential game with controlled jump-diffusion driven state is\nconsidered, and studied using a combination of dynamic programming and\nviscosity solution techniques. We prove, under certain conditions, that the\nvalue of the game exists and is the unique viscosity solution of a fully\nnonlinear integro-partial differential equation. In addition, we formulate and\nprove a verification theorem for such games within the viscosity solution\nframework for nonlocal equations\n

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