COMPARISON OF FIRST-TO-DIE AND LAST-SURVIVOR JOINT LIFE INSURANCE UNDER COMMON SHOCK - Neva Satyahadewi; Louis Putra Jaya; Hendri Kurniawan; Yuyun Eka Pratiwi (BAREKENG: Jurnal Ilmu Matematika dan Terapan, 2026)
Joint life insurance is a type of life insurance policy that covers two individuals, typically a married couple, under a single contract. The benefit is paid either upon the first death (First-to-Die) or after both individuals have passed away (Last-Survivor), depending on the policy type. This study explores the comparative analysis of First-to-Die and Last-Survivor joint life insurance policies under the impact of Common Shock. Common Shock refers to external catastrophic events, such as accidents or natural disasters, that simultaneously increase the mortality risk of both insured individuals. In this study, the Common Shock effect is parameterized by assigning additional joint mortality probabilities ranging from 2.5% to 10%, with increments of 2.5%. A total of 8 scenarios were tested. The first four scenarios vary the Common Shock probabilities at 2.5%, 5.0%, 7.5%, and 10.0%, while keeping the Interest Rate constant at 6.25%. The remaining four scenarios vary the Interest Rates at 5.50%, 5.75%, 6.00%, and 6.25%, with the Common Shock probability fixed at 10.0%. The analysis is conducted through actuarial modeling using present value formulas to assess total insurance premiums under these varying conditions. Using a benefit value of IDR 500,000,000.00 and a premium payment period of 10 years, this study demonstrates how these factors influence premium amounts. The incorporation of Common Shock into premium calculations offers a more realistic perspective in assessing insurance risk and cost. Mortality assumptions are based on the 2023 Indonesian Mortality Table published by BPJS Kesehatan, and the present value of future benefits is calculated using the specified interest rates. The findings reveal that the First-to-Die policy consistently results in significantly higher total premiums compared to the Last-Survivor policy under the same assumptions. On average across all scenarios, the total premium for First-to-Die is 5.67 times greater, primarily due to the higher probability of earlier benefit claims and shorter investment durations from the insurer’s perspective. The First-to-Die policy is more suitable for those with chronic illnesses or financial dependents, while the Last-Survivor policy is preferable for individuals focused on legacy planning.