Hostname: page-component-68945f75b7-72kh6 Total loading time: 0 Render date: 2024-08-05T18:51:42.649Z Has data issue: false hasContentIssue false
  • English
  • Français

Extreme Value Theory and Large Fire Losses

Published online by Cambridge University Press:  29 August 2014

G. Ramachandran
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 7 , Issue 3 , March 1974 , pp. 293 - 310
Copyright
Copyright © International Actuarial Association 1974

References

[1]Gumbel, E. J. (1958). Statistics of extremes. Columbia University Press, New York.CrossRefGoogle Scholar
[2]Thepaut, A. (1950). Le traite d'excédent du coût moyen relatif (ECOMOR). Bull. trimest. Inst. Actu. Fr., 49, 273–343.Google Scholar
[3]Beard, R. E. (1955). Some statistical aspects of non-life insurance. J. Inst. Actu. Students' Soc., 13, Part 3, 139–57.Google Scholar
[4]Beard, R. E. (1963). Some notes on the statistical theory of extreme values. Astin Bull., Vol. III, Pt. I, 6–12.CrossRefGoogle Scholar
[5]D'Hooge, L. (1965). Theorie des valeurs extrêmes et la tarification de “P” excess of loss. Astin. Bull., Vol. III, Pt. II, 163–177.Google Scholar
[6]Jung, J. (1965). On the use of extreme values to estimate the premium for excess of loss reinsurance. Astin Bull., Vol. III, Pt. II, 178–184.Google Scholar
[7]Ramachandran, G. (1972). Extreme value theory and fire losses—further results. Department of the Environment and Fire Offices' Committee Joint Fire Research Organisation Fire Research Note No. 910.Google Scholar
[8]Franckx, E. (1963). Sur la fonction de distribution du sinistre le plus élevé. Astin Bull., Vol. II, Pt. III, 415.CrossRefGoogle Scholar
[9]Benkert, L. G. and Sternberg, I. (1957). An attempt to find an expression for the distribution of fire damage amount. Trans. 15th International Congress of Actuaries, 2, 288–294.Google Scholar
[10]Mandelbrot, B. (1964). Random walks, fire damage amount and other Paretian risk phenomena. Ops Res., 12, 582–585.CrossRefGoogle Scholar
[11]Benkert, L. G. (1963). The log normal model for the distribution of one claim. Astin Bull., Vol. II, Pt. I, 9–23.Google Scholar
[12]Benktander, G. (1963). A note on the most ‘dangerous’ and skewest class of distributions. Astin Bull., Vol. II, Pt. III, 387.CrossRefGoogle Scholar
[13]Ramachandran, G. (1970). Some possible applications of the theory of extreme values for the analysis of fire loss data. Ministry of Technology and Fire Offices' Committee Joint Fire Research Organisation Fire Research Note 837.Google Scholar
[14] United Kingdom fire statistics 1967. London 1969. Her Majesty's Stationery Office.Google Scholar
[15]Ramachandran, G. (1969). The Poisson process and fire loss distribution. Thirty-seventh session of the International Statistical Institute, London.Google Scholar
[16]Ogawa, J. (1951). Contributions to the theory of systematic statistics, I. Osaka Math. J., 3, 175–213.Google Scholar
[17]Sarhan, A. E. and Greenberg, B. G. (Eds) (1962). Contributions to Order Statistics. John Wiley, New York.Google Scholar
[18]Lloyd, E. H. (1952). Least-squares estimation of location and scale parameters using order statistics. Biometrika, 39, 88–95.CrossRefGoogle Scholar