Nonzero-Sum Risk-Sensitive Stochastic Differential Games: A Multi-parameter Eigenvalue Problem Approach

2022/06/24 by Mrinal Kanti Ghosh, K. Suresh Kumar, Ghosh, Mrinal K. +5 · 1 citation
Economics, Econometrics and Finance · Social Sciences · #Economic theories and models #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2206.12067

openalex publication_date 2022/06/24 · openalex created_date 2022/06/29 · openalex updated_date 2026/07/28

Abstract

We study nonzero-sum stochastic differential games with risk-sensitive ergodic cost criterion. Under certain conditions, using multi-parameter eigenvalue approach, we establish the existence of a Nash equilibrium in the space of stationary Markov strategies. We achieve our results by studying the relevant systems of coupled HJB equations. Exploiting the stochastic representation of the principal eigenfunctions we completely characterize Nash equilibrium points in the space of stationary Markov strategies.

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• Ergodic McKean-Vlasov Games: Verification Theorems and Linear-Quadratic Applications

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