Process-based risk measures and risk-averse control of discrete-time systems

• 成果类型: Article
• 署名作者: Fan, Jingnan; Ruszczynski, Andrzej
• 署名单位: Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-018-1349-2
• 发表日期: 2022
• 页码: 113-140
• 关键词: markov decision-processes; stochastic programs; sensitive control; variance; dominance; utility; Consistency; criterion; policies; THEOREM

摘要

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main feature is that they measure risk of processes that are functions of the history of a base process. We introduce a new concept of conditional stochastic time consistency and we derive the structure of process-based risk measures enjoying this property. We show that they can be equivalently represented by a collection of static law-invariant risk measures on the space of functions of the state of the base process. We apply this result to controlled Markov processes and we derive dynamic programming equations. We also derive dynamic programming equations for multistage stochastic programming with decision-dependent distributions.