Endowment Life Insurance Calculation Modeling with DARA Utility Function and Stochastic Interest

Abstract

In this research, a 10-year endowment life insurance’s premium will be calculated with a DARA function according to principle of utility equivalence. The calculation results will be performed using a Vasicek interest-based model, among male and female policyholders within the age range of 20-80 years old, and over varying benefit levels. Indonesian Mortality Table IV 2019 is used as reference for mortality data. Stochastic interest is modeled using the Vasicek Model derived through Ordinary Least Square Method (OLS) Method from BI-Rate in the volatile September 2022 - August 2024 period with a monthly step time, which yields the following parameters: , , , resulting in a 95% confidence interval  with standard error . This  indicated high uncertainty in the interest modelling. The results showed that premium rate is heavily affected by this volatility in the interest rates. Premium value is higher for male than female policyholders and it increases faster at higher entry age due to an increase of the mortality rate. The relation between the DARA coefficient and premium value is non-linear despite a slight increase in premium when a larger coefficient is chosen. An increase of benefit rate is followed by a nearly proportional increase of the premium rate. Further research on this topic could analyze the impact of policy horizon and wealth on the premium rate or compare the results with another stochastic model (e.g. CIR model).