Optimal XL-insurance under Wasserstein-type ambiguity

Birghila, C. & Pflug, G. ORCID: https://orcid.org/0000-0001-8215-3550 (2019). Optimal XL-insurance under Wasserstein-type ambiguity. Insurance: Mathematics and Economics 88 30-43. 10.1016/j.insmatheco.2019.05.005.

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Abstract

We study the problem of optimal insurance contract design for risk management under a budget constraint. The contract holder takes into consideration that the loss distribution is not entirely known and therefore faces an ambiguity problem. For a given set of models, we formulate a minimax optimization problem of finding an optimal insurance contract that minimizes the distortion risk functional of the retained loss with premium limitation. We demonstrate that under the average value-at-risk measure, the entrance-excess of loss contracts are optimal under ambiguity, and we solve the distributionally robust optimal contract-design problem. It is assumed that the insurance premium is calculated according to a given baseline loss distribution and that the ambiguity set of possible distributions forms a neighborhood of the baseline distribution. To this end, we introduce a contorted Wasserstein distance. This distance is finer in the tails of the distributions compared to the usual Wasserstein distance.

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