Monash University
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General Insurance Premiums when Tail Fatness Is Unknown: a Fat Premium Representation Theorem

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journal contribution
posted on 2017-10-23, 07:08 authored by Gay, Roger
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.


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Department of Econometrics and Business Statistics

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