Risk-sensitive Nonzero-sum Stochastic Differential Game with Unbounded Coefficients

2014/12/03 by Saïd Hamadène, Said Hamadène, Rui Mu +2 · 2 citations
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Economic theories and models #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Stochastic processes and financial applications #math.OC

paper · pdf · doi:10.48550/arxiv.1412.1213

arxiv created 2014/12/03 · openalex publication_date 2014/12/03 · arxiv updated 2014/12/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This article is related to risk-sensitive nonzero-sum stochastic differential games in the Markovian framework. This game takes into account the attitudes of the players toward risk and the utility is of exponential form. We show the existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The main tool is the notion of backward stochastic differential equation, which in our case, is multidimensional with continuous generator involving both a quadratic term of Z and a stochastic linear growth component with respect to Z.

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