Abstract

In this talk we study the optimal insurance problem within the risk minimization framework and from a decision maker (DM)'s perspective. We assume that the DM is uncertain about the underlying distribution of her loss and would consider all the distributions that closely surround a given (benchmark) distribution, where the ``closeness" is measured by the L^2 or L^1 distance. Under the expected-value premium principle, the DM picks the indemnity function that minimizes its risk exposure under the worst-case loss distribution. By assuming that the DM's preferences are given by a convex distortion risk measure, we disentangle the structures of the optimal indemnity function and worst-case loss distribution in an analytical way, and give the explicit forms for both of them under specific distortion risk measures. We also compare the results under the $L^2$ distance with the first-order Wasserstein (L^1) distance. Some numerical examples are presented at the end to show more implications of our main results.

About the speaker

姜文骏，加拿大卡尔加里大学数学与统计系助理教授。他于2019年从加拿大西安大略大学统计精算系取得统计博士学位（精算方向）。他主要从事于最有再保险和风险分摊方向的研究。其成果主要发表于IME，Austin Bulletin，SAJ，NAAJ以及EJOR上。