Working Papers 2003 – Abstracts
General Insurance Premiums When Tail Fatness Is Unknown: A Fat Premium Representation Theorem
Roger Gay
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.
Keywords: Order statistics, constant relative risk-averse premiums,
tail-fatness parameter, beta densities
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