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The Power Principle and Tail-Fatness Uncertainty

Author

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  • Roger Gay

Abstract

When insurance claims are governed by fat-tailed distributions, gross uncertainty about the value of the tail-fatness index is virtually inescapable. In this paper a new premium principle (the power principle) analogous to the exponential principle for thin-tailed claims, is discussed. Pareto premiums determined under the principle have a transparent ratio structure, cater convincingly for uncertainty in the tail-fatness index, and are applicable in passage to the extremal limit, to all fat-tailed distributions in the domain of attraction of the (Frechet) extreme-value distribution. Cover can be provided for part claims if existence of the claims mean is in doubt. Stop-loss premiums are also discussed. Mathematical requirements are very modest.

Suggested Citation

  • Roger Gay, 2004. "The Power Principle and Tail-Fatness Uncertainty," Monash Econometrics and Business Statistics Working Papers 1/04, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2004-1
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2004/wp1-04.pdf
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    More about this item

    Keywords

    Exponential principle; power principle; constant risk aversion; ratio premium; stop-loss insurance;
    All these keywords.

    JEL classification:

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

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