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Pareto-optimal reinsurance under individual risk constraints

Author

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  • Ghossoub, Mario
  • Jiang, Wenjun
  • Ren, Jiandong

Abstract

This paper studies the design of Pareto-optimal reinsurance contracts in a market where the insurer and reinsurer maximize their expected utilities of end-of-period wealth. In addition, we assume that the insurer and reinsurer wish to control their solvency risks, which are defined through distortion risk measures of their end-of-period risk exposures. To prevent ex post moral hazard, the no-sabotage condition is exogenously imposed on the set of ex ante admissible indemnity functions. By adopting piece-wise linear distortion functions for the risk measures, we partition the domain of the loss into disjoint pieces as per the features of distortion functions and then derive the parametric form of the optimal indemnity function over each piece, where the parameters are left for numerical optimizations. A concrete example where both the insurer and reinsurer apply Range Value-at-Risk is studied in detail.

Suggested Citation

  • Ghossoub, Mario & Jiang, Wenjun & Ren, Jiandong, 2022. "Pareto-optimal reinsurance under individual risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 307-325.
    • Handle: RePEc:eee:insuma:v:107:y:2022:i:c:p:307-325
    DOI: 10.1016/j.insmatheco.2022.09.003
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    References listed on IDEAS

    as
    1. Chi, Yichun & Zhuang, Sheng Chao, 2020. "Optimal insurance with belief heterogeneity and incentive compatibility," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 104-114.
    2. Chi, Yichun, 2019. "On The Optimality Of A Straight Deductible Under Belief Heterogeneity," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 243-262, January.
    3. Jaume Belles‐Sampera & Montserrat Guillén & Miguel Santolino, 2014. "Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 121-134, January.
    4. Hung-Hsi Huang, 2006. "Optimal insurance contract under a value-at-risk constraint," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(2), pages 91-110, December.
    5. 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.
    6. Gur Huberman & David Mayers & Clifford W. Smith Jr., 1983. "Optimal Insurance Policy Indemnity Schedules," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 415-426, Autumn.
    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. Guillaume Carlier & Rose-Anne Dana, 2003. "Pareto efficient insurance contracts when the insurer's cost function is discontinuous," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 871-893, June.
    9. Assa, Hirbod, 2015. "On optimal reinsurance policy with distortion risk measures and premiums," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 70-75.
    10. Chunyang Zhou & Chongfeng Wu, 2009. "Optimal Insurance Under the Insurer's VaR Constraint," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 34(2), pages 140-154, December.
    11. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2020. "Optimal Insurance under Maxmin Expected Utility," Papers 2010.07383, arXiv.org.
    12. Zhuang, Sheng Chao & Weng, Chengguo & Tan, Ken Seng & Assa, Hirbod, 2016. "Marginal Indemnification Function formulation for optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 65-76.
    13. Mario Ghossoub, 2017. "Arrow's Theorem of the Deductible with Heterogeneous Beliefs," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(1), pages 15-35, January.
    14. 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.
    15. Mario Ghossoub, 2016. "Optimal Insurance with Heterogeneous Beliefs and Disagreement about Zero-Probability Events," Risks, MDPI, vol. 4(3), pages 1-28, August.
    16. Hung-Hsi Huang, 2006. "Optimal insurance contract under a value-at-risk constraint," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(2), pages 91-110, December.
    17. Yichun Chi & Wei Wei, 2020. "Optimal insurance with background risk: An analysis of general dependence structures," Finance and Stochastics, Springer, vol. 24(4), pages 903-937, October.
    18. repec:dau:papers:123456789/5394 is not listed on IDEAS
    19. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "Convex ordering for insurance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 409-416.
    20. Chi, Yichun & Tan, Ken Seng, 2011. "Optimal Reinsurance under VaR and CVaR Risk Measures: a Simplified Approach," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 487-509, November.
    21. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    22. Chi, Yichun & Tan, Ken Seng, 2021. "Optimal Incentive-Compatible Insurance With Background Risk," ASTIN Bulletin, Cambridge University Press, vol. 51(2), pages 661-688, May.
    23. Boonen, Tim J. & Ghossoub, Mario, 2019. "On the existence of a representative reinsurer under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 209-225.
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    More about this item

    Keywords

    Reinsurance; Pareto optimality; Risk constraints; Distortion risk measures; Range Value-at-Risk;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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