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Stochastic representation under g-expectation and applications: The discrete time case

Author

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  • Grigorova, Miryana

    (Center for Mathematical Economics, Bielefeld University)

  • Li, Hanwu

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper, we address the stochastic representation problem in discrete time under (non-linear) g-expectation. We establish existence and uniqueness of the solution, as well as a characterization of the solution. As an application, we investigate a new approach to the optimal stopping problem under g-expectation and the related pricing of American options under Knightian uncertainty. Our results are also applied to a (non-linear) Skorokhod-type obstacle problem.

Suggested Citation

  • Grigorova, Miryana & Li, Hanwu, 2025. "Stochastic representation under g-expectation and applications: The discrete time case," Center for Mathematical Economics Working Papers 721, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:721
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    File URL: https://pub.uni-bielefeld.de/download/3005284/3005285
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    References listed on IDEAS

    as
    1. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    2. Patrick Beissner & Qian Lin & Frank Riedel, 2020. "Dynamically consistent alpha‐maxmin expected utility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1073-1102, July.
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