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Effect of Makeham Mortality Law on Life Insurance Premium Calculations

Abstract

The Makeham mortality law is an actuarial mortality model that describes the force of mortality as a combination of an age-independent component and an age-dependent component. The model provides a mathematical approach for representing mortality patterns that increase with age while also accounting for a constant component of mortality risk. In life insurance, mortality assumptions are essential because they determine the probabilities of survival and death used in estimating future benefit payments and calculating appropriate insurance premiums. This study will examine the effect of the Makeham mortality law on life insurance premium calculations. It will assess how the mortality pattern generated by the Makeham model influences survival probabilities, death probabilities, expected benefit payments, and actuarial present values used in premium determination. The study will also examine how changes in the parameters of the Makeham law affect calculated premiums for different ages, policy durations, and benefit structures. The study will focus on the Makeham mortality law, force of mortality, mortality parameters, survival probabilities, death probabilities, life insurance premiums, actuarial present values, mortality tables, policy duration, age at entry, and interest rate assumptions. Actuarial life table functions and mathematical mortality models will be applied to estimate mortality and survival patterns under the Makeham framework. Premium calculations will then be performed to determine the financial implications of the resulting mortality estimates. A quantitative actuarial research approach will be adopted for the study. Mortality data from standard life tables will be used to estimate or calibrate relevant Makeham mortality parameters. Actuarial present value techniques, life table functions, mathematical modelling, comparative analysis, and sensitivity analysis will be employed to calculate life insurance premiums under the Makeham mortality law. Alternative mortality assumptions may also be considered to evaluate differences in the resulting premium estimates. The study is expected to reveal that the Makeham mortality law may have a significant effect on life insurance premium calculations because changes in the assumed mortality force directly influence expected future claims and actuarial present values. The effect may be more noticeable across different age groups and policy durations where mortality rates change substantially with age. Variations in the Makeham parameters, interest rates, benefit amounts, and policy terms are also expected to produce corresponding changes in premium estimates. The study will be useful to actuaries, life insurance companies, underwriters, pricing analysts, valuation specialists, regulators, and actuarial science researchers. It may provide useful information on the application of the Makeham mortality law in life insurance pricing and assist practitioners in understanding the sensitivity of premium calculations to mortality model parameters. The findings may also support the selection and application of appropriate mortality models for life insurance products. The study concludes that the Makeham mortality law provides an important mathematical framework for incorporating both constant and age-related mortality components into life insurance premium calculations. It is therefore recommended that insurers and actuarial practitioners carefully evaluate the suitability of Makeham mortality parameters against available mortality experience and consider the sensitivity of premium estimates to changes in mortality and financial assumptions.

Keywords: Makeham mortality law, life insurance premiums, mortality modelling, force of mortality, mortality parameters, survival probabilities, death probabilities, actuarial present value, mortality tables, life insurance pricing, actuarial valuation, policy duration, age at entry, interest rate assumptions, premium calculation.