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Optimal Multiple Stopping Problem under Nonlinear Expectation

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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
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    References listed on IDEAS

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    1. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268, April.
    2. N. Meinshausen & B. M. Hambly, 2004. "Monte Carlo Methods For The Valuation Of Multiple‐Exercise Options," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 557-583, October.
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