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