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The utility-based shortfall risk (SR) measure introduced by Folmer and Schied[15] has been recently extended by Mao and Cai [29] to cumulative prospecttheory (CPT) based SR in order to better capture a decision maker'sutility/risk preference. In this paper, we consider a situation whereinformation on the value function and/or the weighting functions in the CPTbased SR is incomplete. Instead of using partially available information toconstruct an approximate value function and weighting functions, we propose arobust approach to define a generalized shortfall risk which is based on atuple of the worst case value/weighting functions from ambiguity sets ofplausible value/weighting functions identified via available information. Theambiguity set may be constructed with elicited preference information (e.g.pairwise comparison questionnaires) and subjective judgement, and the ambiguityreduces as more and more preference information is obtained. Under somemoderate conditions, we demonstrate how the subproblem of the robust shortfallrisk measure can be calculated by solving a linear programming problem. Toexamine the performance of the proposed robust model and computational scheme,we carry out some numerical experiments and report preliminary test results.This work may be viewed as an extension of recent research of preference robustoptimization models to the CPT based SR.

Preference Robust Generalized Shortfall Risk Measure Based on the  Cumulative Prospect Theory When the Value Function and Weighting Functions  Are Ambiguous