专题研讨与学术报告

Preference Robust Distortion Risk Measure

日期：2021-08-04 点击：_showDynClicks("wbnews", 1431088312, 3025)

**报告人：**徐慧福教授 香港中文大学

**时间：**8月7日10:20-11:00

**腾讯会议：**318 5948 4852 密码：8266

**邀请人：**陈志平教授 西安交通大学

**个人简介：**Huifu Xu is a Professor of the Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong. Prior to joining CUHK, he was a professor of Operational Research in the School of Mathematical Sciences, University of Southampton and the Director of the Centre of Operational Research, Management Science and Information Technology (2016-2018). Huifu Xu’s current research is on optimal decision making under uncertainty such as preference robust optimization and distributionally robust optimization which are associated with ambiguity in decision maker’s utility preference or risk attitude and distribution of exogenous uncertainty data. His focus is on developing robust models and computational methods for these problems and applying them in finance, engineering and management sciences. He has published more than 70 papers in the international journals of operational research and optimization including more than 30 papers in Mathematical Programming, SIAM Journal on Optimization, Mathematics of Operations Research and Operations Research. He gives plenary or semi-plenary talks at conferences including the most recent 14th international conference on stochastic programming in Buzios, and the 11th national conference on mathematical optimization of China in Guilin. He is an associate editor of Computational Management Science and Linear algebra, Control and Optimization.

**报告题目：**Preference Robust Distortion Risk Measure

**报告摘要：**Distortion risk measure (DRM) plays a crucial role in risk measuring and managing, especially in insurance pricing. Various DRMs have been introduced but little is discussed about which DRM at hand should be chosen to address a decision maker's risk attitude. In this work, we aim 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 attitude 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 principals such as concavity and inverse S-shapedness of distortion functions (over-weighting on events from impossible to possible or possible to certainty and under-weighting 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 envelop 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 non-decreasing piece-wise 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.

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