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Optimal Multiple Stopping Problem under Nonlinear Expectation

Author

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  • Li, Hanwu

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper, we study the optimal multiple stopping problem under the filtration consistent nonlinear expectations. The reward is given by a set of random variables satisfying some appro- priate assumptions rather than an RCLL process. We first construct the optimal stopping time for the single stopping problem, which is no longer given by the first hitting time of processes. We then prove by induction that the value function of the multiple stopping problem can be interpret- ed as the one for the single stopping problem associated with a new reward family, which allows us to construct the optimal multiple stopping times. If the reward family satisfies some strong regularity conditions, we show that the reward family and the value functions can be aggregated by some progressive processes. Hence, the optimal stopping times can be represented as hitting times.

Suggested Citation

  • Li, Hanwu, 2025. "Optimal Multiple Stopping Problem under Nonlinear Expectation," Center for Mathematical Economics Working Papers 718, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:718
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    File URL: https://pub.uni-bielefeld.de/download/3005043/3005044
    File Function: First Version, 2023
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