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Distributionally Robust Insurance with the Wasserstein Distance
This paper studies 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 Wasserstein 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 first-order and second-order Wasserstein distance. Some numerical examples are given at the end to show more implications of our main results.
Date and Time
-
Language of Oral Presentation
English
Language of Visual Aids
English

Speaker

Edit Name Primary Affiliation
Wenjun Jiang University of Calgary