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Optimal multiple stopping problem with irregular reward

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  14 July 2025

Hanwu Li Open the ORCID record for Hanwu Li [Opens in a new window]
Hanwu Li*
Affiliation:
Shandong University
*
*Postal address: Research Center for Mathematics and Interdisciplinary Sciences, Binhai Rd 72, Qingdao, China; Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Binhai Rd 72, Qingdao, China. Email: lihanwu@sdu.edu.cn
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Abstract

In this paper we study the optimal multiple stopping problem with weak regularity for the reward, where the reward is given by a set of random variables indexed by stopping times. When the reward family is upper semicontinuous in expectation along stopping times, we construct the optimal multiple stopping strategy using the auxiliary optimal single stopping problems. We also obtain the corresponding results when the reward is given by a progressively measurable process.

Keywords

Optimal stoppingoptimal multiple stoppingswing options

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

Information

Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 16
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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