Sistem Bonus Malus dengan Frekuensi Klaim Berdistribusi Geometrik dan Ukuran Klaim Berdistribusi Weibull

Abstract

Bonus-Malus system is one of systems implemented by an insurance in calculating the risk premium based on claim history from each policyholder. In this work we discussed two different types of Bonus-Malus system namely the classical Bonus-Malus system and the optimal Bonus-Malus systems. The classical Bonus-Malus system sets the risk premium by taking into account only the number of accidents of each policyholder. While the optimal Bonus-Malus system sets the risk premium by taking into account both the frequency and the severity of the claims of each policyholder. Both of the Bonus-Malus systems are then compared, with the number and size of the claims and insured persons are assumed to follow respectively a geometric and a Weibull distributions. The risks faced by each policyholder are different such that the number and size of the claims experienced by each policyholder are also different. Fu r t h e rmo r e , posterior distribution o f severity and frequency claim parameters is estimated by using Bayes method. Subsequently, solutions of both systems are obtained in term of future premium based on claim history from each policyholder.