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Optimality of Excess-Loss Reinsurance under a Mean-Variance Criterion

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  • Danping Li
  • Dongchen Li
  • Virginia R. Young

Abstract

In this paper, we study an insurer's reinsurance-investment problem under a mean-variance criterion. We show that excess-loss is the unique equilibrium reinsurance strategy under a spectrally negative L\'{e}vy insurance model when the reinsurance premium is computed according to the expected value premium principle. Furthermore, we obtain the explicit equilibrium reinsurance-investment strategy by solving the extended Hamilton-Jacobi-Bellman equation.

Suggested Citation

  • Danping Li & Dongchen Li & Virginia R. Young, 2017. "Optimality of Excess-Loss Reinsurance under a Mean-Variance Criterion," Papers 1703.01984, arXiv.org, revised Mar 2017.
    • Handle: RePEc:arx:papers:1703.01984
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    References listed on IDEAS

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    Cited by:

    1. Lv Chen & David Landriault & Bin Li & Danping Li, 2021. "Optimal dynamic risk sharing under the time‐consistent mean‐variance criterion," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 649-682, April.
    2. Cao, Jingyi & Landriault, David & Li, Bin, 2020. "Optimal reinsurance-investment strategy for a dynamic contagion claim model," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 206-215.
    3. Chen, Lv & Shen, Yang, 2019. "Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 120-137.
    4. Yan, Tingjin & Park, Kyunghyun & Wong, Hoi Ying, 2022. "Irreversible reinsurance: A singular control approach," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 326-348.
    5. Guan, Guohui & Li, Bin, 2022. "Equilibrium investment and reinsurance strategies under smooth ambiguity with a general second-order distribution," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    6. Li, Peng & Zhou, Ming & Yao, Dingjun, 2022. "Optimal time for the excess of loss reinsurance with fixed costs," International Review of Economics & Finance, Elsevier, vol. 79(C), pages 466-475.
    7. Yan Zhang & Peibiao Zhao & Rufei Ma, 2022. "Robust Optimal Excess-of-Loss Reinsurance and Investment Problem with more General Dependent Claim Risks and Defaultable Risk," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2743-2777, December.
    8. Zhang, Liming & Li, Bin, 2021. "Optimal reinsurance under the α-maxmin mean-variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 225-239.
    9. Zhang, Caibin & Liang, Zhibin, 2022. "Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    10. Zhu, Huainian & Cao, Ming & Zhang, Chengke, 2019. "Time-consistent investment and reinsurance strategies for mean-variance insurers with relative performance concerns under the Heston model," Finance Research Letters, Elsevier, vol. 30(C), pages 280-291.

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