IDEAS home Printed from https://ideas.repec.org/a/eee/jeborg/v180y2020icp638-656.html
   My bibliography  Save this article

Optimal insurance in the presence of multiple policyholders

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167268120300500
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jebo.2020.02.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, March.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Boonen, Tim J. & Liu, Fangda, 2022. "Insurance with heterogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    2. 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.
    3. 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.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sun, Haoze & Weng, Chengguo & Zhang, Yi, 2017. "Optimal multivariate quota-share reinsurance: A nonparametric mean-CVaR framework," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 197-214.
    2. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance without the nonnegativity constraint on indemnities," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 22-39.
    3. Zhu, Yunzhou & Chi, Yichun & Weng, Chengguo, 2014. "Multivariate reinsurance designs for minimizing an insurer’s capital requirement," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 144-155.
    4. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "The optimal insurance under disappointment theories," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 77-90.
    5. Lu, Zhiyi & Meng, Shengwang & Liu, Leping & Han, Ziqi, 2018. "Optimal insurance design under background risk with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 15-28.
    6. Lu, ZhiYi & Liu, LePing & Meng, ShengWang, 2013. "Optimal reinsurance with concave ceded loss functions under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 46-51.
    7. Cui, Wei & Yang, Jingping & Wu, Lan, 2013. "Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 74-85.
    8. Mi Chen & Wenyuan Wang & Ruixing Ming, 2016. "Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle," Risks, MDPI, vol. 4(4), pages 1-12, December.
    9. Hu, Xiang & Yang, Hailiang & Zhang, Lianzeng, 2015. "Optimal retention for a stop-loss reinsurance with incomplete information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 15-21.
    10. Centeno, M.L. & Guerra, M., 2010. "The optimal reinsurance strategy -- the individual claim case," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 450-460, June.
    11. Zhu, Yunzhou & Zhang, Lixin & Zhang, Yi, 2013. "Optimal reinsurance under the Haezendonck risk measure," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1111-1116.
    12. Sung, K.C.J. & Yam, S.C.P. & Yung, S.P. & Zhou, J.H., 2011. "Behavioral optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 418-428.
    13. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2019. "Risk-adjusted Bowley reinsurance under distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 64-72.
    14. Boonen, Tim J. & Liu, Fangda, 2022. "Insurance with heterogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    15. Guerra, M. & de Moura, A.B., 2021. "Reinsurance of multiple risks with generic dependence structures," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 547-571.
    16. 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.
    17. Asimit, Alexandru V. & Badescu, Alexandru M. & Cheung, Ka Chun, 2013. "Optimal reinsurance in the presence of counterparty default risk," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 690-697.
    18. Pierre Picard, 2016. "A Note on Health Insurance under Ex Post Moral Hazard," Risks, MDPI, vol. 4(4), pages 1-9, October.
    19. Wakker, Peter P & Thaler, Richard H & Tversky, Amos, 1997. "Probabilistic Insurance," Journal of Risk and Uncertainty, Springer, vol. 15(1), pages 7-28, October.
    20. Asimit, Alexandru V. & Chi, Yichun & Hu, Junlei, 2015. "Optimal non-life reinsurance under Solvency II Regime," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 227-237.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jeborg:v:180:y:2020:i:c:p:638-656. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jebo .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.