PROPORTIONAL HAZARD TRANSFORM DALAM MENENTUKAN PREMI ASURANSI - Azmi, Azmul
Compound model may be used to model total claims or aggregate claims random variable. To determine the risk premium or the risk-adjusted premium, there are a number of risk measures which may be used. In this final project (tugas akhir), the risk premium is determined by using proportional hazard transform where the risk premium is equal to the proportional hazard mean (PH-mean). In this final project, the PH-mean of the amount of claims random variable is determined by Monte Carlo simulation. Five probability models for amount of claims, of which each PH-mean is discussed, are: gamma, lognormal, loglogistics, Weibull and Pareto. It is assumed that each of the mean and variance of those five probability models are equal and the PH-mean for each distribution is determined using r ? 0,5; r ? 0,8; and r ? 0,95 . For the number of claims random variable, it is assumed that it follows a Poisson distribution. It found that the results from simulations are similar to those obtained theoretically. Firstly, the PH-mean of the amount of claims random variable and the PH-mean of the number of claims random variable are greater than the respective expected values. Secondly, for a smaller index (close to zero), the PH-mean will be larger; where as for a larger index (close to one), the PH-mean will be closer to the expected value. Based on a case study, it is obtained that in determining the PH-mean, for a light tail distribution, it is recommended that an index which is close to one is used; and for a heavy tail distribution, it is recommended that an index which is close to zero is used.