Risk-Sensitive Nonzero-Sum Stochastic Differential Game with Unbounded Coefficients

Said Hamadène () and Rui Mu ()
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Said Hamadène: Université du Maine
Rui Mu: Soochow University

Dynamic Games and Applications, 2021, vol. 11, issue 1, No 4, 84-108

Abstract: 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 towards risks, and the utilities are of exponential forms. 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 and a stochastic linear growth component with respect to the volatility process.

Keywords: Risk-sensitive; Nonzero-sum stochastic differential games; Nash equilibrium point; Backward stochastic differential equations (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13235-020-00353-0

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