ESTIMATING PURE TERM LIFE INSURANCE PREMIUM BASED ON GOMPERTZ-MAKEHAM DISTRIBUTION USING VASICEK MODEL

• Main Author: Widyatna, Ulva
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/69246
• Institution: Institut Teknologi Bandung

The insurance industry is a form of risk transfer that provides mitigation services to cover losses, especially financial losses. In insurance, there are agreements and obligations between the insurer and the insured. The insurer's responsibility is to pay several benefits as a guarantee for the insured party, while the insured's commitment is to pay a premium periodically by the agreement of both parties. Bonuses are influenced by several factors, such as the nominal value of the policy, the term of protection, the probability of death, and the interest rate. In premium calculations, interest rate movements are usually assumed to be constant for ease of analysis. However, this assumption is different in the actual condition that interest rates fluctuate so that, the movement of interest rates is modeled stochastically through the Vasicek model for a more realistic calculation. The probability of death will be calculated using the Gompertz-Makeham distribution with three parameters based on age and factors other than age. Therefore, this study was conducted to estimate the premium for pure term life insurance based on the Gompertz-Makeham distribution in Mortality Table IV by considering interest rate fluctuations using the Vasicek model on BI 7-Days-RR interest rate data. Based on the approximation carried out by the Gompertz-Makeham distribution function for TMI IV, there is a perfect match under the age of 65 years for the male sex while for the female sex under 67 years. Over 65 years (male) and 67 years (female), the estimated probability of death in the Gompertz-Makeham distribution was higher than the probability of dying in TMI IV, but the difference was not significant. The value of ????/01230 ( = 0,6094143 while male ????1230 ( = 0,65207; this number is smaller than the value of ????42530 ( so that the Gompertz-Makeham distribution can best approximate TMI IV. In addition, the results of pure premium calculations using the Vasicek model and the Gompertz-Makeham distribution show that premiums will increase in period with an increase in the individual mortality probability, individuals with old age would pay higher premiums.