Distributionally robust reinsurance with expectile

Xinqiao Xie, Haiyan Liu, Tiantian Mao and Xiao Bai Zhu

ASTIN Bulletin, 2023, vol. 53, issue 1, 129-148

Abstract: We study a distributionally robust reinsurance problem with the risk measure being an expectile and under expected value premium principle. The mean and variance of the ground-up loss are known, but the loss distribution is otherwise unspecified. A minimax problem is formulated with its inner problem being a maximization problem over all distributions with known mean and variance. We show that the inner problem is equivalent to maximizing the problem over three-point distributions, reducing the infinite-dimensional optimization problem to a finite-dimensional optimization problem. The finite-dimensional optimization problem can be solved numerically. Numerical examples are given to study the impacts of the parameters involved.

Date: 2023
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