Time-consistent approximations of risk-averse multistage stochastic optimization problems

• 成果类型: Article
• 署名作者: Asamov, Tsvetan; Ruszczynski, Andrzej
• 署名单位: Princeton University; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0813-x
• 发表日期: 2015
• 页码: 459-493
• 关键词: acceptability measures

摘要

In this paper we study the concept of time consistency as it relates to multistage risk-averse stochastic optimization problems on finite scenario trees. We use dynamic time-consistent formulations to approximate problems having a single coherent risk measure applied to the aggregated costs over all time periods. The dual representation of coherent risk measures is used to create a time-consistent cutting plane algorithm. Additionally, we also develop methods for the construction of universal time-consistent upper bounds, when the objective function is the mean-semideviation measure of risk. Our numerical results indicate that the resulting dynamic formulations yield close approximations to the original problem.