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Distributionally Robust Reinsurance with Glue Value-at-Risk and Expected Value Premium

Author

Listed:
  • Wenhua Lv

    (School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, China)

  • Linxiao Wei

    (College of Science, Wuhan University of Technology, Wuhan 430070, China)

Abstract

In this paper, we explore a distributionally robust reinsurance problem that incorporates the concepts of Glue Value-at-Risk and the expected value premium principle. The problem focuses on stop-loss reinsurance contracts with known mean and variance of the loss. The optimization problem can be formulated as a minimax problem, where the inner problem involves maximizing over all distributions with the same mean and variance. It is demonstrated that the inner problem can be represented as maximizing either over three-point distributions under some mild condition or over four-point distributions otherwise. Additionally, analytical solutions are provided for determining the optimal deductible and optimal values.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3923-:d:1240532
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    References listed on IDEAS

    as
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