Annals of Operations Research

, Volume 237, Issue 1–2, pp 263–279 | Cite as

A simple insurance model: optimal coverage and deductible

Article

Abstract

An insurance model, with realistic assumptions about coverage, deductible and premium, is studied. Insurance is shown to decrease the variance of the cost to the insured, but increase the expected cost, a tradeoff that places our model in the Markowitz mean-variance model.

Keywords

Insurance Optimal coverage Deductible Markowitz mean-variance model 

References

  1. Arrow, K. (1974). Optimal insurance and generalized deductibles. Scandinavian Actuarial Journal, 1, 1–42. CrossRefGoogle Scholar
  2. Bortoluzzo, A. (2011). Estimating total claim size in the auto insurance industry: a comparison between Tweedie and zero-adjusted inverse Gaussian distribution. BAR, Brazilian Administration Review, Curitiba, 8(1). Available from http://www.scielo.br/scielo.php, access on 09 Dec. 2012.
  3. Casualty Actuarial Society, Enterprise Risk Management Committee (2003). Overview of Enterprise Risk Management, May 2003. Google Scholar
  4. COSO (2004). Enterprise Risk Management-Integrated Framework Executive Summary, Committee of Sponsoring Organizations of the Treadway Commission. Google Scholar
  5. Cummins, J. D., & Mahul, O. (2004). The demand for insurance with an upper limit on coverage. The Journal of Risk and Insurance, 71, 253–264. CrossRefGoogle Scholar
  6. Dionne, G. (Ed.) (2000). Handbook of insurance. Boston: Kluwer Academic. Google Scholar
  7. Gollier, C., & Schlesinger, H. (1996). Arrow’s theorem on the optimality of deductibles: A stochastic dominance approach. Economic Theory, 7, 359–363. Google Scholar
  8. Hewitt, C. C. Jr., & Lefkowitz, B. (1979). Methods for fitting distributions to insurance loss data, in Proceedings of the casualty actuarial society, LXVI, pp. 139–160. Google Scholar
  9. Jorgensen, B., & De Souza, M. C. P. (1994). Fitting Tweedie’s compound Poisson model to insurance claims data. Scandinavian Actuarial Journal, 69–93. Google Scholar
  10. Machina, M. J. (1995). Non-expected utility and the robustness of the classical insurance paradigm. The Geneva Papers on Risk and Insurance Theory, 20, 9–50. CrossRefGoogle Scholar
  11. Markowitz, H. M. (1952). Portfolio selection. The Journal of Finance, 7, 77–91. Google Scholar
  12. Markowitz, H. M. (1959). Portfolio selection: efficient diversification of investments. New York: Wiley. Google Scholar
  13. New Jersey Auto Insurance Buyer’s Guide A-705(4/10) (2011) Google Scholar
  14. Olson, D. L., & Wu, D. (2010). Enterprise risk management models. Berlin: Springer. CrossRefGoogle Scholar
  15. Pashigian, B. P., Schkade, L. L., & Menefee, G. H. (1966). The selection of an optimal deductible for a given insurance policy. The Journal of Business, 39, 35–44. CrossRefGoogle Scholar
  16. Raviv, A. (1979). The design of an optimal insurance policy. The American Economic Review, 69, 84–96. Google Scholar
  17. Schlesinger, H. (1981). The optimal level of deductibility in insurance contracts. The Journal of Risk and Insurance, 48, 465–481. CrossRefGoogle Scholar
  18. Schlesinger, H. (1997). Insurance demand without the expected–utility paradigm. The Journal of Risk and Insurance, 64, 19–39. CrossRefGoogle Scholar
  19. Smith, V. (1968). Optimal insurance coverage. Journal of Political Economy, 76, 68–77. CrossRefGoogle Scholar
  20. Smyth, G. K., & Jorgensen, B. (2002). Fitting Tweedie’s compound Poisson model to insurance claims data: dispersion modeling. ASTIN Bulletin, 32, 143–157. CrossRefGoogle Scholar
  21. Wu, D., Olson, D., & Birge, J. (2011). Introduction to special issue on “Enterprise risk management in operations”. International Journal of Production Economics, 134, 1–2. CrossRefGoogle Scholar
  22. Zhou, C., Wu, W., & Wu, C. (2010). Optimal insurance in the presence of insurer’s loss limit. Insurance. Mathematics & Economics, 46, 300–307. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Rutgers Center for Operations ResearchNew BrunswickUSA
  2. 2.Rutgers Center for Operations Research and School of BusinessNew BrunswickUSA

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