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Optimal insurance with divergent beliefs about total default risk

Author

Listed:
  • John David Cummins

    (The Wharton School - University of Pennsylvania)

  • Olivier Mahul

Abstract

This paper extends the classic expected utility theory analysis of optimal insurance contracting to the case where the insurer has a positive probability of total default and the buyer and insurer have divergent beliefs about this probability. The optimal marginal indemnity above the deductible is smaller (greater) than one if the buyer's assessment of default risk is more pessimistic (optimistic) than the insurer's. As an application of the model, we consider the market for reinsurance against catastrophic property loss and propose an expected utility theory explanation for the increasing and concave marginal indemnity schedule observed in this market.

Suggested Citation

  • John David Cummins & Olivier Mahul, 2003. "Optimal insurance with divergent beliefs about total default risk," Post-Print hal-01952121, HAL.
    • Handle: RePEc:hal:journl:hal-01952121
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    Citations

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    Cited by:

    1. Stephens, Eric & Thompson, James R., 2014. "CDS as insurance: Leaky lifeboats in stormy seas," Journal of Financial Intermediation, Elsevier, vol. 23(3), pages 279-299.
    2. Jiazhen Peng & Xiaojun Shan & Yang Gao & Yohannes Kesete & Rachel Davidson & Linda Nozick & Jamie Kruse, 2014. "Modeling the integrated roles of insurance and retrofit in managing natural disaster risk: a multi-stakeholder perspective," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 74(2), pages 1043-1068, November.
    3. Stephens, Eric & Thompson, James, 2012. "Separation Without Mutual Exclusion in Financial Insurance," Working Papers 2012-8, University of Alberta, Department of Economics.
    4. Boonen, Tim J. & Liu, Fangda, 2022. "Insurance with heterogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    5. 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.
    6. Denis-Alexandre Trottier & Van Son Lai & Anne-Sophie Charest, 2017. "CAT Bond Spreads Via HARA Utility and Nonparametric Tests," Working Papers 2017-002, Department of Research, Ipag Business School.
    7. Eric LANGLAIS, 2008. "On Insurance Contract Design For Low Probability Events," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(2(4)_Summ).
    8. Radoslav Raykov, 2015. "Catastrophe insurance equilibrium with correlated claims," Theory and Decision, Springer, vol. 78(1), pages 89-115, January.
    9. Eric Langlais, 2008. "On insurance contract design for low probability events," Working Papers hal-04140722, HAL.
    10. 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.
    11. Strauss, Jason, 2007. "Equilibrium in the Insurance Industry: Price and Probability of Insolvency," MPRA Paper 11015, University Library of Munich, Germany.
    12. Enrico Biffis & Erik Chavez & Alexis Louaas & Pierre Picard, 2022. "Parametric insurance and technology adoption in developing countries," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 47(1), pages 7-44, March.
    13. Glenn W. Harrison & Jia Min Ng, 2018. "Welfare effects of insurance contract non-performance," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 39-76, May.
    14. Markus Huggenberger & Peter Albrecht, 2022. "Risk pooling and solvency regulation: A policyholder's perspective," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 907-950, December.
    15. Strauss, Jason, 2006. "The Impact of Price Controls on Mandatory Automobile Insurance Markets," MPRA Paper 11016, University Library of Munich, Germany.
    16. Biener, Christian & Landmann, Andreas & Santana, Maria Isabel, 2019. "Contract nonperformance risk and uncertainty in insurance markets," Journal of Public Economics, Elsevier, vol. 175(C), pages 65-83.
    17. Johannes G. Jaspersen & Richard Peter & Marc A. Ragin, 2023. "Probability weighting and insurance demand in a unified framework," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 48(1), pages 63-109, March.
    18. Eric Stephens & James R. Thompson, 2015. "Separation Without Exclusion in Financial Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 82(4), pages 853-864, December.
    19. Feria-Domínguez, José Manuel & Jiménez-Rodríguez, Enrique & Sholarin, Ola, 2015. "Tackling the over-dispersion of operational risk: Implications on capital adequacy requirements," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 206-221.
    20. Boonen, Tim J., 2019. "Equilibrium recoveries in insurance markets with limited liability," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 38-45.
    21. Strauss, Jason, 2007. "Price Regulation, Market Exit, and Financial Leverage of Canadian Property-Liability Insurers," MPRA Paper 11212, University Library of Munich, Germany, revised 28 Oct 2008.
    22. Yohannes Kesete & Jiazhen Peng & Yang Gao & Xiaojun Shan & Rachel A. Davidson & Linda K. Nozick & Jamie Kruse, 2014. "Modeling Insurer‐Homeowner Interactions in Managing Natural Disaster Risk," Risk Analysis, John Wiley & Sons, vol. 34(6), pages 1040-1055, June.
    23. Peter, Richard & Ying, Jie, 2020. "Do you trust your insurer? Ambiguity about contract nonperformance and optimal insurance demand," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 938-954.
    24. José S. Penalva, 2003. "A Study of the Interaction of Insurance and Financial Markets: Efficiency and Full Insurance Coverage," Working Papers 286, Barcelona School of Economics.

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