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

Author

Listed:
  • Said Hamadène

    (Université du Maine)

  • Rui Mu

    (Soochow University)

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.

Suggested Citation

  • Said Hamadène & Rui Mu, 2021. "Risk-Sensitive Nonzero-Sum Stochastic Differential Game with Unbounded Coefficients," Dynamic Games and Applications, Springer, vol. 11(1), pages 84-108, March.
    • Handle: RePEc:spr:dyngam:v:11:y:2021:i:1:d:10.1007_s13235-020-00353-0
    DOI: 10.1007/s13235-020-00353-0
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    References listed on IDEAS

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    1. Hu, Ying & Tang, Shanjian, 2016. "Multi-dimensional backward stochastic differential equations of diagonally quadratic generators," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1066-1086.
    2. El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
    3. Hamidou Tembine & Quanyan Zhu & Tamer Basar, 2011. "Risk-sensitive mean field stochastic differential games," Post-Print hal-00643547, HAL.
    4. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    5. Xing, Hao & Žitković, Gordan, 2018. "A class of globally solvable Markovian quadratic BSDE systems and applications," LSE Research Online Documents on Economics 73440, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Chen, Fang & Guo, Xianping, 2023. "Two-person zero-sum risk-sensitive stochastic games with incomplete reward information on one side," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 218-245.

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