Penaksiran Cadangan Dana pada Asuransi Kendaraan Bermotor Melalui Pendekatan Bayesian; Model Banyaknya Klaim: Poisson-Gamma dan Model Ganti Rugi: Lognormal-Inversχ^2-Normal

Abstract

In the motor vehicle insurance market, insurance companies need to know an estimate of the number of claims and the value of compensation they will face in the next policy period, and need to estimate the aggregate payment. In this study, the number of claims is assumed to have a Poisson distribution and the compensation value is assumed to be of a Lognormal distribution. Bayesian sensibilities will be used in shaping the predictive distribution of aggregate payments. Therefore, the Gamma distribution is used as the prior Poisson distribution, while the prior distribution of Lognormal is the Inverse χ ^ 2 distribution and the Normal distribution. The purpose of this paper is to provide an estimate of adequate reserve funds for motor vehicle insurance companies. Estimates of reserve funds are obtained from percentiles of the distribution of aggregate payments. Monte Carlo simulation techniques are used to estimate the aggregate distribution of payments. The test results show that the Poisson and Lognormal models are suitable in modeling the real data used in this paper. The simulation results from the predictive distribution show that the 95th percentile is IDR 404,368,169, so that this value can be used as an estimate of adequate reserve funds. The results of this study are expected to provide new information that is useful for motor vehicle insurance companies when estimating adequate reserve funds.