Comparison of Zillmer and Premium Sufficiency Reserve Method using the Vasicek Stochastic Interest Rate Model

Abstract

An accurate calculation of premium reserves will ensure that the insurance company can pay claims. Premium reserves are funds collected by insurance companies which are the difference between the sum insured and the value of payments during the insurance period prepared for claim payments. There are several methods for calculating premium reserves, but the methods that are the focus of this study are the Zillmer method and the Premium Sufficiency method, extensions of the prospective method. This study aims to compare the two methods using the Vasicek model to determine the stochastic interest rate. Then the Ordinary Least Square method is used to estimate the Vasicek interest rate parameter. In comparing the two premium reserve methods, this study builds a simulation for reference male and female insureds using Bank Indonesia reference rate data for 2017-2021 and the Indonesian Mortality Table IV from 2019. The results of this study indicate that premiums reserve calculations using the Zillmer method yield less value than the Premium Adequacy method for both male and female insureds.