Mathematical Model of Joint Life Term Insurance Premiums under Inflation, Interest Rate, and Dependent Mortality

Ine Febrianti Habel; I Gusti Putu Purnaba; Retno Budiarti

doi:10.31764/jtam.v10i2.35690

Mathematical Model of Joint Life Term Insurance Premiums under Inflation, Interest Rate, and Dependent Mortality

Ine Febrianti Habel, I Gusti Putu Purnaba, Retno Budiarti

Abstract

Multilife insurance refers to a contract that covers two or more lives simultaneously, with joint life insurance representing a key form in which the benefit is paid upon the first death among the insured individuals. The lifetimes of insured individuals are typically not independent, as they may be influenced by shared environmental, health, or behavioral factors, leading to mortality dependence. Inflation and interest rates also play critical roles in determining the present value of benefits and premiums. However, most previous studies have examined either mortality dependence or macroeconomic effects in isolation. This study aims to develop a comprehensive mathematical model for determining joint life term insurance premiums that simultaneously incorporates mortality dependence through the Gumbel copula and interest rate and inflation through the Fisher equation. The model integrates demographic and economic risk components within a unified actuarial valuation framework, providing a more realistic representation of premium dynamics under varying financial conditions. Simulation results indicate that premiums incorporating inflation are consistently higher than those without inflation, whereas higher nominal interest rates result in lower premium levels. These findings reflect the theoretical relationship between inflation, real interest rates, and the time value of money. The study further introduces an elasticity-based analysis that quantifies the sensitivity of premiums to changes in inflation and interest rates, demonstrating nonlinear yet economically meaningful responses across different age structures of insured spouses. The results highlight the importance of jointly modeling mortality dependence and economic variables to enhance pricing accuracy and fairness in life insurance. The proposed model offers practical relevance for actuaries in premium determination, assists insurers in risk management and product design, and supports the development of resilient pricing strategies under inflationary and interest.

Keywords

Dependent mortality; Inflation; Interest rate; Joint life; Term insurance.

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DOI: https://doi.org/10.31764/jtam.v10i2.35690