A comparison between two kinds of BMS based on different credibility

Abstract

The paper develops a design of optimal Bonus-Malus System (BMS) based on exact equitable credibility.in which the relative error function is taken as toss function. In BMS,both the frequency and lhe severity componems are considered. This design is compared with traditional BMS derived from classical squared-error loss function. w 1 IntroductionIn automobile insurance, when setting premiums, inequities will necessarily arise when,due to imperfect information,some policyholders are charged more than they should be and others less. At the same time,it will incur a loss to the insurer. To deal with this problem,BMS is widely used.In classical credibility theoryt~:,the loss function is taken to be the traditional squared error. I.emaire >j developed a BMS based only on the number of claims of each policyholder. Each policyholder has to pay a premium proportional to his unknown claim frequency. The use of the estimated claim frequency instead of the true unknown claim frequency will incur a loss to the insurer. To minimize this loss,Lemaire r'~: considered the optimal BMS obtained using the quadratic error loss function,the expected-value premium calculation principle and Poisson-Gamma as 1he claim frequency distribution. Dionne and Vanassa ~el took the characleristics of each individual such as the age variable into consideration. Suppose ~hat age has a negative effect on the expected number of claims,it would imply that insurance premiums should decrease with age. Frangos and Vrontos ::~:designed an optimal BMS with both a frequency and a severity, using Poisson-Gamma as the claim frequency distribution and Exponential-Inveres Gamma as the severity distribution. To minimize the insurer's risk,they used the squared-error loss function and took into account simultaneously the number of claims and the level of severity of each Received : 2003-12-03. M R Sub jeer Crass ifica t ion : 62C 12.