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Optimal Reinsurance Design: A Mean-Variance Approach

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  • Yichun Chi
  • Ming Zhou

Abstract

In this article, we study an optimal reinsurance model from the perspective of an insurer who has a general mean-variance preference. In order to reduce ex post moral hazard, we assume that both parties in a reinsurance contract are obligated to pay more for a larger realization of loss. We further assume that the reinsurance premium is calculated only based on the mean and variance of the indemnity. This class of premium principles is quite general in the sense that it includes many widely used premium principles such as expected value, mean value, variance, and standard deviation principles. Moreover, to protect the insurer's profit, a lower bound is imposed on its expected return. We show that any admissible reinsurance policy is dominated by a change-loss reinsurance or a dual change-loss reinsurance, depending upon the coefficient of variation of the ceded loss. Further, the change-loss reinsurance is shown to be optimal if the premium loading increases in the actuarial value of the coverage; while it becomes decreasing, the optimal reinsurance policy is in the form of dual change loss. As a result, the quota-share reinsurance is always optimal for any variance-related reinsurance premium principle. Finally, some numerical examples are applied to illustrate the applicability of the theoretical results.

Suggested Citation

  • Yichun Chi & Ming Zhou, 2017. "Optimal Reinsurance Design: A Mean-Variance Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(1), pages 1-14, January.
  • Handle: RePEc:taf:uaajxx:v:21:y:2017:i:1:p:1-14
    DOI: 10.1080/10920277.2016.1192478
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    Cited by:

    1. Chi, Yichun, 2018. "Insurance choice under third degree stochastic dominance," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 198-205.
    2. Chen, Lv & Shen, Yang & Su, Jianxi, 2020. "A continuous-time theory of reinsurance chains," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 129-146.
    3. Xiaoqing Liang & Ruodu Wang & Virginia Young, 2021. "Optimal Insurance to Maximize RDEU Under a Distortion-Deviation Premium Principle," Papers 2107.02656, arXiv.org, revised Feb 2022.

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