A DYNAMIC PROGRAMMING APPROACH TO DISTRIBUTION-CONSTRAINED OPTIMAL STOPPING

• 成果类型: Article
• 署名作者: Kallblad, Sigrid
• 署名单位: Royal Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1724
• 发表日期: 2022
• 页码: 1902-1928
• 关键词: compactness; transport; times

摘要

We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales enables us to transform the distributional constraint into an initial condition and view the problem as a stochastic control problem; we establish the corresponding dynamic programming principle. The method offers a systematic approach for solving the problem for general constraints and under weak assumptions on the cost function. In addition, we provide certain continuity results for the value of the problem viewed as a function of its distributional constraint.