monash_2331.pdf (457.71 kB)
General Insurance Premiums when Tail Fatness Is Unknown: a Fat Premium Representation Theorem
Version 2 2017-10-23, 07:08
Version 1 2017-06-08, 02:32
journal contribution
posted on 2017-10-23, 07:08 authored by Gay, RogerFat-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.
History
Year of first publication
2003Series
Department of Econometrics and Business StatisticsUsage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC