Zero-sum stochastic differential game with risk-sensitive cost

2017/04/10 by Anup Biswas, Biswas, Anup, Subhamay Saha +1
Economics, Econometrics and Finance · Mathematics · #91A15 #Economic theories and models #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #msc:91A15

paper · pdf · doi:10.48550/arxiv.1704.02689

openalex publication_date 2017/04/10 · arxiv created 2018/01/03 · arxiv updated 2018/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Zero sum games with risk-sensitive cost criterion are considered with underlying dynamics being given by controlled stochastic differential equations. Under the assumption of geometric stability on the dynamics , we completely characterize all possible saddle point strategies in the class of stationary Markov controls. In addition, we also establish existence-uniqueness result for the value function of the Hamilton-Jacobi-Isaacs equation.

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