Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping

• 成果类型: Article
• 署名作者: Pichler, Alois; Liu, Rui Peng; Shapiro, Alexander
• 署名单位: Technische Universitat Chemnitz; University System of Georgia; Georgia Institute of Technology
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.2120
• 发表日期: 2022
• 关键词: stochastic programming; Coherent risk measures; time consistency; dynamic equations; optimal stopping time; Snell envelope; inventory model; American put option

摘要

This paper addresses time consistency of risk-averse optimal stopping in stochastic optimization. It is demonstrated that time-consistent optimal stopping entails a specific structure of the functionals describing the transition between consecutive stages. The stopping risk measures capture this structural behavior and allow natural dynamic equations for risk-averse decision making over time. Consequently, associated optimal policies satisfy Bellman's principle of optimality, which characterizes optimal policies for optimization by stating that a decision maker should not reconsider previous decisions retrospectively. We also discuss numerical approaches to solving such problems.