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Published in: Dynamic Games and Applications 1/2021

15-04-2020

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

Authors: Said Hamadène, Rui Mu

Published in: Dynamic Games and Applications | Issue 1/2021

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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.

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Metadata
Title
Risk-Sensitive Nonzero-Sum Stochastic Differential Game with Unbounded Coefficients
Authors
Said Hamadène
Rui Mu
Publication date
15-04-2020
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 1/2021
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-020-00353-0

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