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A BSDE approach to stochastic differential games with incomplete information

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  • Grün, Christine

Abstract

We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our aim is to quantify the amount of information the informed player has to reveal in order to play optimally: to do so, we show that the value function of this zero-sum game can be rewritten as a minimization problem over some martingale measures with a payoff given by the solution of a backward stochastic differential equation.

Suggested Citation

  • Grün, Christine, 2012. "A BSDE approach to stochastic differential games with incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1917-1946.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1917-1946
    DOI: 10.1016/j.spa.2012.02.010
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    References listed on IDEAS

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    1. Pierre Cardaliaguet & Catherine Rainer, 2009. "On a Continuous-Time Game with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 769-794, November.
    2. repec:dau:papers:123456789/6935 is not listed on IDEAS
    3. repec:dau:papers:123456789/6927 is not listed on IDEAS
    4. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, April.
    5. 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.
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    Cited by:

    1. Fabien Gensbittel & Catherine Rainer, 2018. "A Two-Player Zero-sum Game Where Only One Player Observes a Brownian Motion," Dynamic Games and Applications, Springer, vol. 8(2), pages 280-314, June.

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