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EXPANSION IN BELL POLYNOMIALS OF THE DISTRIBUTION OF THE TOTAL CLAIM AMOUNT WITH WEIBULL-DISTRIBUTED CLAIM SIZES

Part of: Mathematical economics

Published online by Cambridge University Press:  01 April 2008

RAMON LACAYO
RAMON LACAYO*
Affiliation:
Escuela de Ingeniería Comercial, Universidad Católica del Norte, Larrondo 1281, Coquimbo, Chile (email: rlacayo@ucn.cl)
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Abstract

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The total claim amount for a fixed period of time is, by definition, a sum of a random number of claims of random size. In this paper we explore the probabilistic distribution of the total claim amount for claims that follow a Weibull distribution, which can serve as a satisfactory model for both small and large claims. As models for the number of claims we use the geometric, Poisson, logarithmic and negative binomial distributions. In all these cases, the densities of the total claim amount are obtained via Laplace transform of a density function, an expansion in Bell polynomials of a convolution and a subsequent Laplace inversion.

Keywords

Laplace transformBell polynomialtotal claim amountclaim size processclaim number processprobability density function

MSC classification

Secondary: 91B30: Risk theory, insurance
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 4 , April 2008 , pp. 495 - 501
Copyright
Copyright © Australian Mathematical Society 2008

References

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