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15. The Design of an Optimal Bonus-Malus System Based on the Sichel Distribution

  • 2014
  • OriginalPaper
  • Chapter
Published in:
Authors
George Tzougas
Nicholas Frangos
Published in
Modern Problems in Insurance Mathematics
Publisher
Springer International Publishing

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Abstract

This chapter presents the design of an optimal Bonus-Malus System (BMS) using the Sichel distribution to model the claim frequency distribution. This system is proposed as an alternative to the optimal BMS obtained by the traditional Negative Binomial model [19]. The Sichel distribution has a thicker tail than the Negative Binomial distribution and it is considered as a plausible model for highly dispersed count data. We also consider the optimal BMS provided by the Poisson-Inverse Gaussian distribution (PIG), which is a special case of the Sichel distribution. Furthermore, we develop a generalised BMS that takes into account both the a priori and a posteriori characteristics of each policyholder. For this purpose we consider the generalised additive models for location, scale and shape (GAMLSS) in order to use all available information in the estimation of the claim frequency distribution. Within the framework of the GAMLSS we propose the Sichel GAMLSS for assessing claim frequency as an alternative to the Negative Binomial Type I (NBI) regression model used by Dionne and Vanasse [9, 10]. We also consider the NBI and PIG GAMLSS for assessing claim frequency.

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previous chapter The Impact of Stress Factors on the Price of Widow’s Pensions
next chapter Bonus-Malus Systems in Open and Closed Portfolios
Title
The Design of an Optimal Bonus-Malus System Based on the Sichel Distribution
Authors
George Tzougas
Nicholas Frangos
Copyright Year
2014
Book
Modern Problems in Insurance Mathematics

Print ISBN: 978-3-319-06652-3

Electronic ISBN: 978-3-319-06653-0

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-06653-0_15
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