An Inverse Optimal Stopping Problem for Diffusion Processes

• 成果类型: Article
• 署名作者: Kruse, Thomas; Strack, Philipp
• 署名单位: University of Duisburg Essen; University of California System; University of California Berkeley
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0930
• 发表日期: 2019
• 页码: 423-439
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; quickest detection; reflection; OPTION; drift; time

摘要

Let X be a one-dimensional diffusion and let g be a real-valued function depending on time and the value of X. This article analyzes the inverse optimal stopping problem of finding a time-dependent real-valued function pi depending only on time such that a given stopping time tau(star) is a solution of the stopping problem sup(tau) E[g(tau, X-tau) + pi(tau)]. Under regularity and monotonicity conditions, there exists such a transfer pi if and only if tau(star) is the first time when X exceeds a time-dependent barrier b. We prove uniqueness of the solution pi and derive a closed form representation. The representation is based on an auxiliary process that is a version of the original diffusion X reflected at b toward the continuation region. The results lead to a new integral equation characterizing the stopping boundary b of the stopping problem sup(tau) E[g(tau, X-tau)].