General Insurance Premiums when Tail Fatness Is Unknown: a Fat Premium Representation Theorem Gay, Roger 10.4225/03/5938b727eb8dc https://bridges.monash.edu/articles/journal_contribution/General_Insurance_Premiums_when_Tail_Fatness_Is_Unknown_a_Fat_Premium_Representation_Theorem/5090569 Fat-tailed distributions are used to model claims on general insurance contracts under which extremely large claims are a very real possibility. Since estimation of the tail-fatness parameter is notoriously difficult - it is one of the major outstanding statistical/actuarial problems - methods which do not require precise knowledge are valuable. A characteristic feature of an important class of fat-tailed distributions, Pareto, is that ratios of expected values of large claims in the form {1+E[X(n)]}/{1+E[X(n-k)]} are independent of sample size. For suitably modelled uncertainty about the tail-fatness parameter, premiums to insurers with constant relative risk aversion can be represented in terms of these ratios. Premiums increase with the insurers' risk-aversion and depend upon their perception of the fattest-tailed distribution generating claims. 2017-10-23 07:08:33 Order statistics 1959.1/2331 monash:2331 2003 constant relative risk-averse premiums tail-fatness parameter beta densities