TY - CHAP

T1 - The design of an optimal bonus-malus system based on the Sichel distribution

AU - Tzougas, George

AU - Frangos, Nicholas

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Sichel Distribution

KW - Bonus-malus System (BMS)

KW - Generalized Additive Models For Location, Scale And Shape (GAMLSS)

KW - Negative Binomial Inverse Gaussian-Poisson (PIG)

U2 - 10.1007/978-3-319-06653-0_15

DO - 10.1007/978-3-319-06653-0_15

M3 - Chapter (peer-reviewed)

SN - 9783319066523

T3 - EAA Series

SP - 239

EP - 260

BT - Modern Problems in Insurance Mathematics

PB - Springer

ER -