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

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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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Authors and Affiliations

  1. LMM, Université du Maine, Avenue Olivier Messiaen, 72085, Le Mans Cedex 9, France

    Said Hamadène

  2. Center for Financial Engineering and School of Mathematical Sciences, Soochow University, Suzhou, 215006, People’s Republic of China

    Rui Mu

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  1. Said Hamadène
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  2. Rui Mu
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Correspondence to Rui Mu.

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The second author is supported in part by National Natural Science Foundation for Young Scientists of China (Grant No. 11701404) and Natural Science Foundation for Young Scientists of Jiangsu Province of China (Grant No. BK20160300)

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Hamadène, S., Mu, R. Risk-Sensitive Nonzero-Sum Stochastic Differential Game with Unbounded Coefficients. Dyn Games Appl 11, 84–108 (2021). https://doi.org/10.1007/s13235-020-00353-0

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  • DOI: https://doi.org/10.1007/s13235-020-00353-0

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