Journal of Risk and Uncertainty

, Volume 27, Issue 2, pp 121–138 | Cite as

Optimal Insurance With Divergent Beliefs About Insurer Total Default Risk

  • J. David Cummins
  • Olivier MahulEmail author


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.

catastrophe insurance default risk risk perception 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Applied Insurance Research. (1998). Projected Insured Losses from Natural Disasters. Boston.Google Scholar
  2. Arrow, Kenneth. (1963). "Uncertainty and theWelfare Economics of Medical Care," American Economic Review 53, 941–973.Google Scholar
  3. Cummins, J. David, Neil Doherty, and Anita Lo. (2002). "Can Insurers Pay for the "Big One"? Measuring the Capacity of the Insurance Market to Respond to Catastrophic Losses," Journal of Banking and Finance 26, 557–583.Google Scholar
  4. Cummins, J. David, Martin F. Grace, and Richard D. Phillips. (1999). "Regulatory Solvency Prediction in Property-Liability Insurance: Risk-based Capital, Audit Ratios, And Cash Flow Simulation," Journal of Risk and Insurance 66, 417–458.Google Scholar
  5. Cummins, J. David, D. Lalonde, and Richard D. Phillips. (2002). "Managing Risk Using Index-Linked Catastrophic Loss Securities." In M. Lane (ed.), Alternative Risk Strategies. London: Risk Books, pp. 19–46.Google Scholar
  6. Cummins, J. David, Christopher M. Lewis, and Richard D. Phillips. (1999). "Pricing Excess of Loss Reinsurance Contracts Against Catastrophic Loss." In Kenneth A. Froot (ed.), The Financing of Catastrophe Risk. Chicago: University of Chicago Press, pp. 93–148.Google Scholar
  7. Cummins, J. David and Mary A. Weiss. (2000). "The Global Market for Reinsurance: Consolidation, Capacity, and Efficiency," Brookzings-Wharton Papers on Financial Services 2000, 159–209.Google Scholar
  8. Cummins, J. David and Olivier Mahul. (2000). "Managing Catastrophic Risk With Insurance Contracts Subject to Default Risk," NBER Insurance Project Workshop, February 25–26, 2000, Cambridge, MA.Google Scholar
  9. Doherty, Neil. (1997). "Financial Innovation in the Management of Catastrophic Risk," Journal of Applied Corporate Finance 10, 84–95.Google Scholar
  10. Doherty, Neil and Georges Dionne. (1993). "Insurance with Undiversifiable Risk: Contract Structure and Organizational Form of Insurance Firms," Journal of Risk and Uncertainty 6, 187–203.Google Scholar
  11. Doherty, Neil and Harris Schlesinger. (1990). "Rational Insurance Purchasing: Consideration of Contract Nonperformance," Quarterly Journal of Economics 105, 243–253.Google Scholar
  12. Doherty, Neil, and Harry Schlesinger. (2002). "Insurance Contracts and Securitization," Journal of Risk and Insurance 69, 45–62.Google Scholar
  13. Drèze, Jacques. (1987). Essays on Economic Decisions Under Uncertainty. Cambridge: Cambridge University Press.Google Scholar
  14. Froot, Kenneth. (2001). "The Market for Catastrophe Risk: A Clinical Examination," Journal of Financial Economics 60, 529–571.Google Scholar
  15. Froot, Kenneth, David Scharfstein, and Jeremy Stein. (1993). "Risk Management: Coordinating Corporate Investment and Financing Decisions," Journal of Finance 48, 1629–1658.Google Scholar
  16. Gollier, Christian. (1992). "Economic Theory of Risk Exchanges: A Review." In Georges Dionne (ed.), Contributions to Insurance Economics. Norwell, MA: Kluwer Academic Publishers, pp. 3–23.Google Scholar
  17. Gollier, Christian. (2000). "Optimal Insurance Design: What CanWe DoWith andWithout Expected Utility?" In Georges Dionne (ed.), Handbook of insurance. Norwell, MA: Kluwer Academic Publishers, pp. 97–115.Google Scholar
  18. Greenwald, Bruce. C. and Joseph E. Stiglitz. (1993). "Financial Market Imperfections and Business Cycles," Quarterly Journal of Economics 108, 77–114.Google Scholar
  19. Jaffee, Darrell M. and Thomas Russell. (1997). "Catastrophe Insurance, Capital Markets, and Uninsurable Risks," Journal of Risk and Insurance 64, 205–230.Google Scholar
  20. Johnson, Herb, and Rene Stulz. (1987). "The Pricing of Options with Default Risk," Journal of Finance 42, 2267–2280.Google Scholar
  21. Kimball, Miles S. (1990). "Precautionary Savings in the Small and in the Large," Econometrica 58, 53–73.Google Scholar
  22. Klugman, Stuart, Harry Panjer, and Gordon Willmot. (1998). Loss Models: From Data to Decisions. New-York: Wiley-Interscience Publication.Google Scholar
  23. Marshall, John. (1992). "Optimum Insurance with Deviant Beliefs." In Georges Dionne (ed.), Contributions to insurance economics. Boston: Kluwer Academic Publishers, pp. 255–274.Google Scholar
  24. Mossin, Jan. (1968). "Aspects of Rational Insurance Purchasing," Journal of Political Economy 79, 553–568.Google Scholar
  25. Raviv, Arthur. (1979). "The Design of an Optimal Insurance Policy," American Economic Review 69, 84–96.Google Scholar
  26. Schlesinger, Harris. (2000). "The Theory of Insurance Demand." In G. Dionne (ed.), Handbook of Insurance, Kluwer Academic Publishers, pp. 131–151.Google Scholar
  27. Smith, Clifford W. and Rene Stulz. (1985). "The Determinants of Firms' Hedging Policies," Journal of Financial and Quantitative Analysis 20, 391–405.Google Scholar
  28. Tapiero, C., Y. Kahane, and L. Jacque. (1986). "Insurance Premiums and Default Risk in Mutual Insurance," Scandinavian Actuarial Journal 82–97.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  1. 1.The Wharton SchoolUniversity of PennsylvaniaUSA
  2. 2.Department of EconomicsINRARennesFrance

Personalised recommendations