Risk forms: representation, disintegration, and application to partially observable two-stage systems

• 成果类型: Article
• 署名作者: Dentcheva, Darinka; Ruszczynski, Andrzej
• 署名单位: Stevens Institute of Technology; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01376-1
• 发表日期: 2020
• 页码: 297-317
• 关键词: convex; optimization

摘要

We introduce the concept of a risk form, which is a real functional of two arguments: a measurable function on a Polish space and a measure on that space. We generalize the duality theory and the Kusuoka representation to this setting. For a risk form acting on a product of Polish spaces, we define marginal and conditional forms and we prove a disintegration formula, which represents a risk form as a composition of its marginal and conditional forms. We apply the proposed approach to two-stage stochastic programming problems with partial information and decision-dependent observation distribution.