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Effect of Constant Force of Mortality Assumption on Life Insurance Valuation

Abstract

The constant force of mortality assumption is an actuarial approach that assumes the instantaneous rate of mortality remains constant over a specified period. This assumption provides a simplified basis for estimating survival and mortality probabilities and is useful in actuarial calculations where a manageable mortality model is required. In life insurance valuation, mortality assumptions are important because they influence the expected timing and amount of future benefit payments and consequently affect the value of insurance contracts and their associated liabilities. This study will examine the effect of the constant force of mortality assumption on life insurance valuation. It will assess how the assumption influences the estimation of survival probabilities, death probabilities, expected benefit payments, and actuarial present values of life insurance benefits. The study will also consider how the use of a constant mortality force affects the valuation of life insurance contracts compared with mortality patterns that vary with age. The study will focus on constant force of mortality, survival probabilities, mortality rates, life insurance valuation, actuarial present values, life insurance benefits, mortality assumptions, policy duration, age at entry, and interest rate assumptions. Actuarial functions will be applied to estimate expected future benefits under the constant mortality assumption. Different mortality and interest rate assumptions may also be examined to determine their effects on the calculated values of life insurance contracts. A quantitative actuarial research approach will be adopted for the study. Data from standard mortality tables and relevant actuarial assumptions will be used to construct survival and mortality probabilities under the constant force of mortality model. Actuarial present value calculations, life table functions, comparative analysis, sensitivity analysis, and mathematical modelling will be employed to evaluate the effect of the assumption on life insurance valuation. Alternative mortality assumptions may be used as a basis for comparison. The study is expected to reveal that the constant force of mortality assumption may have a significant effect on life insurance valuation, particularly where actual mortality rates vary considerably with age. The assumption may produce different actuarial values from age-dependent mortality models because it applies a uniform mortality intensity across the period considered. The magnitude of the difference is expected to depend on the assumed mortality force, policy duration, age at entry, benefit structure, and interest rate used in the valuation. 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 implications of simplified mortality assumptions for life insurance valuation and assist practitioners in evaluating the suitability of the constant force approach for different insurance contracts. The findings may also contribute to better understanding of mortality assumptions used in actuarial models. The study concludes that the constant force of mortality assumption is an important actuarial modelling approach that can influence the valuation of life insurance contracts through its effect on survival and mortality probabilities. It is therefore recommended that insurers and actuarial practitioners carefully assess the suitability of the constant mortality assumption for the specific policy and population being valued and consider the potential valuation differences arising from more age-sensitive mortality models.

Keywords: Constant force of mortality, life insurance valuation, mortality assumption, survival probability, mortality rate, actuarial present value, life insurance benefits, mortality force, life tables, actuarial modelling, policy duration, age at entry, interest rate, mortality modelling, insurance liabilities.