General Insurance Premiums When Tail Fatness Is Unknown: A Fat Premium Representation Theorem

Roger Gay ()

No 13/03, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: G22 (search for similar items in EconPapers)
Pages: 15 pages
Date: 2003-08
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2003/wp13-03.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:msh:ebswps:2003-13

Ordering information: This working paper can be ordered from
http://business.mona ... -business-statistics

Access Statistics for this paper

More papers in Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics PO Box 11E, Monash University, Victoria 3800, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Professor Xibin Zhang ().