Distributionally robust reinsurance with expectile

作者：Xinqiao Xie, Haiyan Liu, Tiantian Mao, Xiaobai Zhu · 发表于：Astin Bulletin · 年份：2023 · DOI：10.1017/asb.2022.28 · 被引用次数：11 · 研究领域：Risk and Portfolio Optimization、Insurance, Mortality, Demography, Risk Management、Insurance and Financial Risk Management

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.