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Adaptive Premiums for Evolutionary Claims in Non-Life Insurance

Author

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  • Roger Gay

Abstract

Rapid growth in heavy-tailed claim severity in commercial liability insurance requires insurer response by way of flexible mechanisms to update premiums. To this end in this paper a new premium principle is established for heavy-tailed claims, and its properties investigated. Risk-neutral premiums for heavy-tailed claims are consistently and unbiasedly estimated by the ratio of the first two extremes of the claims distribution. That is, the heavy-tailed risk-neutral premium has a Pareto distribution with the same tail-index as the claims distribution. Insurers must predicate premiums on larger tail-index values, if solvency is to be maintained. Additionally, the structure of heavy-tailed premiums is shown to lead to a natural model for tail-index imprecision (demonstrably inescapable in the sample sizes with which we deal). Premiums which compensate for tail-index uncertainty preserve the ratio structure of risk-neutral premiums, but make a 'prudent' adjustment which reflects the insurer's risk-profile. An example using Swiss Re's (1999) major disaster data is used to illustrate application of the methodology to the largest claims in any insurance class.

Suggested Citation

  • Roger Gay, 2004. "Adaptive Premiums for Evolutionary Claims in Non-Life Insurance," Monash Econometrics and Business Statistics Working Papers 25/04, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2004-25
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2004/wp25-04.pdf
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    References listed on IDEAS

    as
    1. Albrecht, Peter, 1992. "Premium Calculation Without Arbitrage? A note on a contribution by G. Venter," ASTIN Bulletin, Cambridge University Press, vol. 22(2), pages 247-254, November.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Insurance Claims; Premiums; Tail-Index; Extreme Values;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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