The design of an optimal Bonus-Malus System based on the Sichel distribution

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

Is investment time irreversible? Some empirical evidence for disaggregated UK manufacturing data

It has long been suggested that investment may be time irreversible, and consideration of the option value of waiting to invest has aroused renewed interest in this issue. This study tests for time irreversibility in UK investment according to disaggregation by type of investment expenditure and across manufacturing sector groupings. The test results reported indicate that the irreversibility of investment patterns varies not only from industry to industry but also according to the type of capital being purchased, with significant time irreversibility detected in gross fixed capital formation and aggregate vehicles expenditure, and industrial sector groupings comprising fuels and oil refining, engineering and vehicles, and textiles and leather. However, only in the first and last of these series is time irreversibility attributable to non-linearities in the underlying data generating process, and consistent with threshold effects which may be associated with (S,s) type models of investment dynamics.