Extreme Value Theory and Large Fire Losses
- 1 March 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in ASTIN Bulletin
- Vol. 7 (3) , 293-310
- https://doi.org/10.1017/s0515036100006115
Abstract
The statistical theory of extreme values well described by Gumbel [1] has been fruitfully applied in many fields, but only in recent times has it been suggested in connection with fire insurance problems. The idea originally stemmed from a consideration of the ECOMOR reinsurance treaty proposed by Thepaut [2]. Thereafter, a few papers appeared investigating the usefulness of the theory in the calculation of an excess of loss premium. Among these, Beard [3, 4], d'Hooge [5] and Jung [6] have made contributions which are worth studying. They have considered, however, only the largest claims during a succession of periods. In this paper, generalized techniques are presented which enable use to be made of all large losses that are available for analysis and not merely the largest. These methods would be particularly useful in situations where data are available only for large losses.Keywords
This publication has 6 references indexed in Scilit:
- Random Walks, Fire Damage Amount and Other Paretian Risk PhenomenaOperations Research, 1964
- Some Notes on the Statistical Theory of Extreme ValuesASTIN Bulletin, 1963
- Sur la fonction de distribution du sinistre le plus eleveASTIN Bulletin, 1963
- A Note on the Most “Dangerous” and Skewest Class of DistributionsASTIN Bulletin, 1963
- Statistics of ExtremesPublished by Columbia University Press ,1958
- LEAST-SQUARES ESTIMATION OF LOCATION AND SCALE PARAMETERS USING ORDER STATISTICSBiometrika, 1952