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Distributionally robust reinsurance with expectile

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

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.

Suggested Citation

  • Xie, Xinqiao & Liu, Haiyan & Mao, Tiantian & Zhu, Xiao Bai, 2023. "Distributionally robust reinsurance with expectile," ASTIN Bulletin, Cambridge University Press, vol. 53(1), pages 129-148, January.
    • Handle: RePEc:cup:astinb:v:53:y:2023:i:1:p:129-148_7
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    Cited by:

    1. Wenhua Lv & Linxiao Wei, 2023. "Distributionally Robust Reinsurance with Glue Value-at-Risk and Expected Value Premium," Mathematics, MDPI, vol. 11(18), pages 1-23, September.

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