The Power Principle and Tail-Fatness Uncertainty
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.
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