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Optimal insurance in the presence of multiple policyholders

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  • Bernard, Carole
  • Liu, Fangda
  • Vanduffel, Steven

Abstract

The literature on optimal insurance typically considers optimal risk sharing between one insurer (or reinsurer) and one insurance prospect. However, the insurance business is based on diversification benefits that arise when pooling many insurance policies. In this paper, we first show that the classical results on optimal insurance in the case of a single insurance prospect remain valid when there are multiple prospects, provided their insurance claims are independent. Specifically, all prospects receive coverage. However, due to phenomena such as medical progress, longevity risk, and natural or man-made disasters, insurance claims tend to be correlated. We show that in the case of interdependent insurance policies, it may become optimal for the insurer to refuse to sell insurance to some prospects, and this decision is driven by the prospects’ attitudes towards risk and their risk exposure characteristics. This finding calls for government policies to ensure that insurance remains available and affordable to everyone.

Suggested Citation

  • Bernard, Carole & Liu, Fangda & Vanduffel, Steven, 2020. "Optimal insurance in the presence of multiple policyholders," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 638-656.
    • Handle: RePEc:eee:jeborg:v:180:y:2020:i:c:p:638-656
    DOI: 10.1016/j.jebo.2020.02.012
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    References listed on IDEAS

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    1. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Cai, Jun & Wei, Wei, 2012. "Optimal reinsurance with positively dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 57-63.
    3. K. C. Cheung & K. C. J. Sung & S. C. P. Yam, 2014. "Risk-Minimizing Reinsurance Protection For Multivariate Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(1), pages 219-236, March.
    4. Ranyard, Rob & McHugh, Sandie, 2012. "Defusing the risk of borrowing: The psychology of payment protection insurance decisions," Journal of Economic Psychology, Elsevier, vol. 33(4), pages 738-748.
    5. Richard N. Rosett, 1976. "The Role of Health Insurance in the Health Services Sector," NBER Books, National Bureau of Economic Research, Inc, number rose76-1.
    6. Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
    7. Kaluszka, Marek, 2004. "An extension of Arrow's result on optimality of a stop loss contract," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 527-536, December.
    8. Erwann O. Michel‐Kerjan & Carolyn Kousky, 2010. "Come Rain or Shine: Evidence on Flood Insurance Purchases in Florida," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 369-397, June.
    9. Charles E. Phelps, 1976. "Demand for Reimbursement Insurance," NBER Chapters, in: The Role of Health Insurance in the Health Services Sector, pages 115-162, National Bureau of Economic Research, Inc.
    10. Carole Bernard & Steven Vanduffel, 2014. "Financial Bounds for Insurance Claims," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(1), pages 27-56, March.
    11. W. Kip Viscusi, 1995. "Government Action, Biases in Risk Perception, and Insurance Decisions," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 20(1), pages 93-110, June.
    12. Kaluszka, Marek, 2001. "Optimal reinsurance under mean-variance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 61-67, February.
    13. J. Francois Outreville, 2014. "Risk Aversion, Risk Behavior, and Demand for Insurance: A Survey," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 37(2), pages 158-186.
    14. Cai, Jun & Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2008. "Optimal reinsurance under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 185-196, August.
    15. Cheung, Ka Chun & Dhaene, Jan & Lo, Ambrose & Tang, Qihe, 2014. "Reducing risk by merging counter-monotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 58-65.
    16. Borch, Karl, 1963. "Recent Developments in Economic Theory and their Application to Insurance," ASTIN Bulletin, Cambridge University Press, vol. 2(3), pages 322-341, April.
    17. Markus K. Brunnermeier, 2004. "Learning to Reoptimize Consumption at New Income Levels: A Rationale for Prospect Theory," Journal of the European Economic Association, MIT Press, vol. 2(1), pages 98-114, March.
    18. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
    19. Denuit, Michel & Vermandele, Catherine, 1998. "Optimal reinsurance and stop-loss order," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 229-233, July.
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    2. David Landriault & Bin Li & Hong Li & Yuanyuan Zhang, 2024. "Contract Structure and Risk Aversion in Longevity Risk Transfers," Papers 2409.08914, arXiv.org.
    3. Zhuo Jin & Zuo Quan Xu & Bin Zou, 2020. "A Perturbation Approach to Optimal Investment, Liability Ratio, and Dividend Strategies," Papers 2012.06703, arXiv.org, revised May 2021.
    4. Reichel, Lukas & Schmeiser, Hato & Schreiber, Florian, 2022. "On the optimal management of counterparty risk in reinsurance contracts," Journal of Economic Behavior & Organization, Elsevier, vol. 201(C), pages 374-394.
    5. Meng, Hui & Wei, Li & Zhou, Ming, 2023. "Multiple per-claim reinsurance based on maximizing the Lundberg exponent," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 33-47.

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