Distributionally robust insurance under the Wasserstein distance

28 Pages Posted: 3 Oct 2024

See all articles by Tim J. Boonen

Tim J. Boonen

University of Hong Kong

Wenjun Jiang

University of Calgary

Date Written: August 19, 2024

Abstract

This paper studies the optimal insurance contracting from the perspective of a decision maker (DM) who has an ambiguous understanding of the loss distribution. The ambiguity set of loss distributions is represented as a p-Wasserstein ball, with p ∈ Z + , centered around a specific benchmark distribution. The DM selects the indemnity function that minimizes the worst-case risk within the risk-minimization framework, considering the constraints of the Wasserstein ball. Assuming that the DM is endowed with a convex distortion risk measure and that insurance pricing follows the expected-value premium principle, we derive the explicit structures of both the indemnity function and the worst-case distribution using a novel survival-function-based representation of the Wasserstein distance. We examine a specific example where the DM employs the GlueVaR and provide numerical results to demonstrate the sensitivity of the worst-case distribution concerning the model parameters.

Keywords: Optimal insurance, robustness, distortion risk measure, Wasserstein distance, Glue-VaR

Suggested Citation

Boonen, Tim J. and Jiang, Wenjun, Distributionally robust insurance under the Wasserstein distance (August 19, 2024). Available at SSRN: https://ssrn.com/abstract=4942336 or http://dx.doi.org/10.2139/ssrn.4942336

Tim J. Boonen

University of Hong Kong ( email )

Pokfulam Road
Hong Kong
China

Wenjun Jiang (Contact Author)

University of Calgary ( email )

University Drive
Calgary, Alberta T2N 1N4
Canada

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