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Pareto‐Optimal Insurance Policies in the Models with a Premium Based on the Actuarial Value

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  • A. Y. Golubin

Abstract

This article analyzes the problem of designing Pareto‐optimal insurance policies when both the insurer and the insured are risk averse and the premium is calculated as a function of the actuarial value of the insurer's risk. Two models are considered: in the first, the set of admissible policies is constrained by a given size of the premium; in the second, the premium size is not constrained so that it varies with the actuarial value of a policy chosen by the agents. For both cases a characterization of the Pareto‐optimal policies is derived. The corresponding optimality equations for the Pareto‐optimal policies are obtained and compared with the results on the classical risk exchange model.

Suggested Citation

  • A. Y. Golubin, 2006. "Pareto‐Optimal Insurance Policies in the Models with a Premium Based on the Actuarial Value," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(3), pages 469-487, September.
    • Handle: RePEc:bla:jrinsu:v:73:y:2006:i:3:p:469-487
    DOI: 10.1111/j.1539-6975.2006.00184.x
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    Cited by:

    1. Borglin, Anders & Flåm, Sjur, 2007. "Risk Exchange as a Market or Production Game," Working Papers 2007:16, Lund University, Department of Economics.
    2. Peng Yang & Zhiping Chen, 2023. "Optimal Private Health Insurance Contract towards the Joint Interests of a Policyholder and an Insurer," Mathematics, MDPI, vol. 11(10), pages 1-28, May.
    3. Carole Bernard & Shaolin Ji & Weidong Tian, 2013. "An optimal insurance design problem under Knightian uncertainty," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(2), pages 99-124, November.
    4. Chen Li & Xiaohu Li, 2018. "On the Optimal Risk Sharing in Reinsurance with Random Recovery Rate," Risks, MDPI, vol. 6(4), pages 1-16, October.
    5. repec:hal:wpaper:hal-00746245 is not listed on IDEAS
    6. Jiang, Wenjun & Hong, Hanping & Ren, Jiandong, 2021. "Pareto-optimal reinsurance policies with maximal synergy," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 185-198.
    7. Jiang, Wenjun & Ren, Jiandong & Yang, Chen & Hong, Hanping, 2019. "On optimal reinsurance treaties in cooperative game under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 173-184.
    8. Zeng, Xudong & Luo, Shangzhen, 2013. "Stochastic Pareto-optimal reinsurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 671-677.
    9. Dutang, Christophe & Albrecher, Hansjoerg & Loisel, Stéphane, 2013. "Competition among non-life insurers under solvency constraints: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 231(3), pages 702-711.
    10. Wenjun Jiang & Jiandong Ren & Ričardas Zitikis, 2017. "Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account," Risks, MDPI, vol. 5(1), pages 1-22, February.
    11. Carole Bernard & Weidong Tian, 2010. "Insurance Market Effects of Risk Management Metrics," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 35(1), pages 47-80, June.
    12. Cai, Jun & Liu, Haiyan & Wang, Ruodu, 2017. "Pareto-optimal reinsurance arrangements under general model settings," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 24-37.
    13. A. Y. Golubin, 2015. "A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 791-803, September.

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