Martingale characterizations of risk-averse stochastic optimization problems

• 成果类型: Article
• 署名作者: Pichler, Alois; Schlotter, Ruben
• 署名单位: Technische Universitat Chemnitz
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01391-2
• 发表日期: 2020
• 页码: 377-403
• 关键词: polar factorization; REPRESENTATION; rearrangement; DECOMPOSITION; PROGRAMS

摘要

This paper addresses risk awareness of stochastic optimization problems. Nested risk measures appear naturally in this context, as they allow beneficial reformulations for algorithmic treatments. The reformulations presented extend usual dynamic equations by involving risk awareness in the problem formulation. Nested risk measures are built on risk measures, which originate by conditioning on the history of a stochastic process. We derive martingale properties of these risk measures and use them to prove continuity. It is demonstrated that stochastic optimization problems, which incorporate risk awareness via nesting risk measures, are continuous with respect to the natural distance governing these optimization problems, the nested distance.