Shortfall Risk Models When Information on Loss Function Is Incomplete

Erick Delage (), Shaoyan Guo () and Huifu Xu ()
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Erick Delage: GERAD and Department of Decision Sciences, HEC Montréal, Montréal, Québec H3T 2A7, Canada
Shaoyan Guo: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Huifu Xu: Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong 999077, Hong Kong

Operations Research, 2022, vol. 70, issue 6, 3511-3518

Abstract: The utility-based shortfall risk (SR) measure effectively captures a decision maker’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 programs when the underlying exogenous uncertainty is discretely distributed.

Keywords: Optimization; preference robust optimization; utility-based shortfall risk measure; preference elicitation; linear programming; tractability (search for similar items in EconPapers)
Date: 2022
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