The Use of Monte Carlo Method to Model the Aggregate Loss Distribution

Abstract

Based on Law Number 24 of 2011, a state program was established to provide social protection and welfare for everyone, one of which is health insurance by the Social Insurance Administration Organization (BPJS). In its implementation, several important evaluations are needed. One that requires accurate evaluation is claim frequency and claim severity in determining premiums and reserved funds. This thesis provides one form of a method for selecting the distribution of claim frequency and claim severity. The data used in this study was taken from BPJS Health in the City of Tangerang in 2017. The distribution of opportunities chosen had been adjusted to the participant's claim data and parameter estimated using the Maximum Likelihood Estimation method. The chi-square test was used to check the goodness of fit for claim frequency distributions whereas the Anderson Darling tests were applied to claim severity distributions. The results of the chi-square test and the Anderson-Darling test showed that the model that matched the claim frequency distribution was the Z12M–NBGE distribution while the model that matched the claim severity was lognormal. The Z12M–NBGE distribution and the lognormal formed the aggregate loss distribution using the Monte Carlo method. Furthermore, the simulation results were obtained to the measurement of the Value in Risk (VaR) and Shortfall Expectations (ES). So, the Monte Carlo method is simple to implement the aggregate loss distributions and can easily handle various risks with dependency.