Preference robust distortion risk measure and its application

Distortion risk measure (DRM) plays a crucial role in management science and finance particularly actuarial science. Various DRMs have been introduced but little is discussed on which DRM at hand should be chosen to address decision maker's (DM's) preference. This paper aims fill out the gap. Specifically, we consider situation where true distortion function unknown either because it difficult identify/elicit and/or DM's preference ambiguous. We introduce robust (PRDRM), based worst-case from an ambiguity set of functions mitigate impact arising ambiguity. The constructed under well-known general principles such as concavity inverse S-shapedness (overweighting events impossible possible or certainty underweighting those more possible) well new user-specific information sensitivity tail losses, confidence intervals some lotteries, preferences certain lotteries over others. To calculate proposed PRDRM, use convex concave envelope points characterize curvature derive tractable reformulation PRDRM when underlying random loss discretely distributed. Moreover, show that nondecreasing piecewise linear can determined by solving programming problem. Finally, apply capital allocation problem carry numerical tests examine efficiency model.