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Numerical approximation of Dynkin games 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 propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric information. The target solution depends on three variables: the time, the spatial (or state) variable, and a variable from a standard (I - 1)-simplex which represents the probabilities with which the I possible configurations of the game are played. The proposed numerical approximation preserves the convexity of the continuous solution as well as the lower and upper obstacle bounds. We show convergence of the fully-discrete scheme to the unique viscosity solution of the continuous problem and present a range of numerical studies to demonstrate its applicability.

Suggested Citation

  • Banas, Lubomir & Ferrari, Giorgio & Randrianasolo, Tsiry Avisoa, 2025. "Numerical approximation of Dynkin games with asymmetric information," Center for Mathematical Economics Working Papers 733, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:733
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    File URL: https://pub.uni-bielefeld.de/download/3006158/3006159
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    References listed on IDEAS

    as
    1. Tiziano De Angelis & Erik Ekström & Kristoffer Glover, 2022. "Dynkin Games with Incomplete and Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 560-586, February.
    2. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    3. Christoph Kühn & Andreas E. Kyprianou, 2007. "Callable Puts As Composite Exotic Options," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 487-502, October.
    4. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
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    Cited by:

    1. Tiziano De Angelis & Jan Palczewski & Jacob Smith, 2025. "Martingale theory for Dynkin games with asymmetric information," Papers 2510.15616, arXiv.org.

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