Shortfall Risk Models When Information on Loss Function Is Incomplete

• 成果类型: Article
• 署名作者: Delage, Erick; Guo, Shaoyan; Xu, Huifu
• 署名单位: Universite de Montreal; HEC Montreal; Universite de Montreal; HEC Montreal; Dalian University of Technology; Chinese University of Hong Kong
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.2212
• 发表日期: 2022
• 页码: 3511-3518
• 关键词: preference robust optimization; utility-based shortfall risk measure; Preference elicitation; linear programming; tractability

摘要

The utility-based shortfall risk (SR) measure effectively captures a decisionmaker's risk attitude on tail losses by an increasing convex loss function. In this paper, we consider a situation where the decision maker's risk attitude toward tail losses is ambiguous and introduce a robust version of SR, which mitigates the risk arising from such ambiguity. Specifically, we use some available partial information or subjective judgement to construct a set of utility-based loss functions and define a so-called preference robust shortfall risk (PRSR) through the worst loss function from the (ambiguity) set. We then apply the PRSR to optimal decision-making problems and demonstrate how the latter can be reformulated as tractable convex programswhen the underlying exogenous uncertainty is discretely distributed.