Penentuan Premi Sistem Bonus Malus dengan Menggunakan Fungsi Utilitas Eksponensial

Abstract

A Bonus Malus system is one of systems used in the automobile insurance. This system introduces the clasification of premium level, which is influenced by the number of claims from the policyholder every year. This paper discusses premium calculation on Bonus Malus system for automobile third party liability insurance with two different methods, which both are based on exponential utility functions. The first method is carried out by applying the principle of zero utility using the exponential utlilty function. The second method is formulated by breaking the symmetry between overcharges and undercharges by weighting them differently in the utility function in order to penalize the overcharges. In order to compare the calculation methods of both approaches, the expected value principle should be given in advance. Number of claims from each policyholder is assumed to follow Poisson distribution, while the parameters follow the gamma distribution. This leads to an unconditional negative binomial distribution. The posterior distribution of frequency claim parameter is to be determined in order to estimate the parameters using Bayes estimation technique. The premium calculation on Bonus Malus system using expected value and zero utility principle implies very high cost for high risk. In the Bonus Malus premium using the penalization of overcharges approach, the ratio between extreme premiums is reduced to produce a smaller Malus. Therefore, the most appropriate premium for policyholder in every class is the premium which applies penalization of overcharges