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Numerical Appromixation of the Value of a Stochastic Differential Game with Asymmetric Information

Author

Listed:
  • Banas, Lubomir

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Randrianasolo, Tsiry Avisoa

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We consider a convexity constrained Hamilton-Jacobi-Bellman-type obstacle problem for the value function of a zero-sum differential game with asymmetric information. We propose a convexity-preserving probabilistic numerical scheme for the approximation of the value function which is discrete w.r.t. the time and convexity variables, and show that the scheme converges to the unique viscosity solution of the considered problem. Furthermore, we generalize the semi-discrete scheme to obtain an implementable fully discrete numerical approximation of the value function and present numerical experiments to demonstrate the properties of the proposed numerical scheme.

Suggested Citation

  • Banas, Lubomir & Ferrari, Giorgio & Randrianasolo, Tsiry Avisoa, 2020. "Numerical Appromixation of the Value of a Stochastic Differential Game with Asymmetric Information," Center for Mathematical Economics Working Papers 630, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:630
    as

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    File URL: https://pub.uni-bielefeld.de/download/2939974/2939975
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    References listed on IDEAS

    as
    1. VIEILLE, Nicolas & ROSENBERG, Dinah & SOLAN, Eilon, 2002. "Stochastic games with a single controller and incomplete information," HEC Research Papers Series 754, HEC Paris.
    2. 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.
    3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    4. MERTENS, Jean-François & ZAMIR, Shmuel, 1971. "The value of two-person zero-sum repeated games with lack of information on both sides," LIDAM Reprints CORE 154, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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