Discussion on “The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking” (by Tzougas et al.)

Excerpt

In their paper, Tzougas, Hoon and Lim use the Negative Binomial Inverse Gaussian (NBIG) regression model to approximate the number of claims in a portfolio of motor TPL contracts—as an alternative to standard approaches, namely mixed Poisson models. This of course is generally relevant in all types of insurance, but it is specifically relevant in motor insurance where premium rates often depend on the claims history of a given insured, i.e. prior claims. Moreover, often the premium will be adapted with hindsight according to numbers of reported claims while the contract is under exposure. For both the initial premium (a priori) and the premium in subsequent years (a posteriori), the number of claims on a contract is the main component of the so-called Bonus Malus Systems (BMS) that have widely been used in motor insurance for decades. The paper not only estimates the proposed and other standard models to approximate claim numbers, but it also applies the results to real data in order to calculate premium rates accordingly and to compare them under standard ratemaking models. The main achievement of the paper then is not to present NBIG as the “better” distribution, in the sense of the fit, but to present an elegant algorithm by which the model can be estimated. The model and algorithm were tested on a sample that contained roughly 146,000 records of a Greek Motor Third Party Liability (MTPL) portfolio written and monitored over a period of 3 years. The rating criteria are named age and “horsepower” of the car (actually it is motor capacity, measured in cubic centimeters), and the size of the city that the insured is a resident of, which is not necessarily the region where the car is being used. Each criterion is clustered into three categories that differ in size. This adds up to a simplified tariff of three one-dimensional criteria consisting of 3 × 3 × 3 = 27 cells in total. …