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Optimal retention for a stop-loss reinsurance with incomplete information

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  • Hu, Xiang
  • Yang, Hailiang
  • Zhang, Lianzeng

Abstract

This paper considers the determination of optimal retention in a stop-loss reinsurance. Assume that we only have incomplete information on a risk X for an insurer, we use an upper bound for the value at risk (VaR) of the total loss of an insurer after stop-loss reinsurance arrangement as a risk measure. The adopted method is a distribution-free approximation which allows to construct the extremal random variables with respect to the stochastic dominance order and the stop-loss order. We derive the optimal retention such that the risk measure used in this paper attains the minimum. We establish the sufficient and necessary conditions for the existence of the nontrivial optimal stop-loss reinsurance. For illustration purpose, some numerical examples are included and compared with the results yielded in Theorem 2.1 of Cai and Tan (2007).

Suggested Citation

  • Hu, Xiang & Yang, Hailiang & Zhang, Lianzeng, 2015. "Optimal retention for a stop-loss reinsurance with incomplete information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 15-21.
    • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:15-21
    DOI: 10.1016/j.insmatheco.2015.08.005
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    References listed on IDEAS

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    Cited by:

    1. Junhong Du & Zhiming Li & Lijun Wu, 2019. "Optimal Stop-Loss Reinsurance Under the VaR and CTE Risk Measures: Variable Transformation Method," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1133-1151, March.
    2. Hu, Xiang & Duan, Baige & Zhang, Lianzeng, 2017. "De Vylder approximation to the optimal retention for a combination of quota-share and excess of loss reinsurance with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 48-55.
    3. Fan, Qi & Tan, Ken Seng & Zhang, Jinggong, 2023. "Empirical tail risk management with model-based annealing random search," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 106-124.
    4. Liu, Haiyan & Mao, Tiantian, 2022. "Distributionally robust reinsurance with Value-at-Risk and Conditional Value-at-Risk," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 393-417.
    5. 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.
    6. Mi Chen & Wenyuan Wang & Ruixing Ming, 2016. "Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle," Risks, MDPI, vol. 4(4), pages 1-12, December.

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