Abstract

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

About the Speaker

王伟博士，本硕毕业于西安交通大学，2023年6月毕业于英国南安普顿大学商学院获得博士学位，现为香港中文大学系统工程与工程管理系助理研究员。王伟博士目前的研究兴趣包括preference robust optimization, decision making under uncertainty, quantitative and qualitative statistical robustness, and risk measure。截止目前，王伟博士已经在European Journal of Operational Research, SIAM journal on Optimization, Mathematical Finance 等国际知名期刊以第一作者发表6篇学术论文。