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1 results

  • Distributionally robust reinsurance with expectile

  • Xinqiao Xie, Haiyan Liu, Tiantian Mao, Xiao Bai Zhu
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 53 / Issue 1 / January 2023
    Published online by Cambridge University Press:
    16 February 2023, pp. 129-148
    Print publication:
    January 2023
    • Article
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  • 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.