Working Papers 2004 – Abstracts
The Power Principle and Tail-Fatness Uncertainty
Roger Gay
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.
Keywords: Exponential principle, power principle, constant risk
aversion, ratio premium, stop-loss insurance
