Discussion of the Danish Data on Large Fire Insurance Losses

AbstractAlexander McNeil's (1996) study of the Danish data on large fire insurance losses provides an excellent example of the use of extreme value theory in an important application context. We point out how several alternate statistical techniques and plotting devices can buttress McNeil's conclusions and provide flexible tools for other studies.

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Extreme Value Theory and Large Fire Losses

Astin Bulletin ◽

10.1017/s0515036100006115 ◽

1974 ◽

Vol 7 (3) ◽

pp. 293-310 ◽

Cited By ~ 12

Author(s):

G. Ramachandran

Keyword(s):

Statistical Theory ◽

Extreme Value Theory ◽

Extreme Values ◽

Value Theory ◽

Extreme Value ◽

Large Fire ◽

Fire Insurance ◽

Reinsurance Treaty

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.

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Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory

Astin Bulletin ◽

10.2143/ast.27.1.563210 ◽

1997 ◽

Vol 27 (1) ◽

pp. 117-137 ◽

Cited By ~ 266

Author(s):

Alexander J. McNeil

Keyword(s):

Extreme Value Theory ◽

Generalized Pareto Distribution ◽

Value Theory ◽

Extreme Value ◽

Parametric Curve ◽

Excess Loss ◽

Generalized Pareto ◽

Fire Insurance ◽

Loss Severity ◽

Parametric Curve Fitting

AbstractGood estimates for the tails of loss severity distributions are essential for pricing or positioning high-excess loss layers in reinsurance. We describe parametric curve-fitting methods for modelling extreme historical losses. These methods revolve around the generalized Pareto distribution and are supported by extreme value theory. We summarize relevant theoretical results and provide an extensive example of their application to Danish data on large fire insurance losses.

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