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A BSDE approach to stochastic differential games with incomplete information

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  • Grün, Christine
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912000324
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 4 ()
    Pages: 1917-1946

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1917-1946

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    Related research

    Keywords: Stochastic differential games; Backward stochastic differential equations; Dynamic programming; Viscosity solutions;

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    1. 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.
    2. Cardaliaguet, Pierre & Rainer, Catherine, 2009. "Stochastic Differential Games with Asymmetric Information," Economics Papers from University Paris Dauphine 123456789/6927, Paris Dauphine University.
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