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Effect of Uniform Distribution of Deaths Assumption on Life Insurance Reserve Estimates

Abstract

The uniform distribution of deaths assumption is an actuarial assumption that treats deaths as occurring evenly throughout a specified period, commonly within each policy year. This assumption is used to simplify the estimation of mortality-related cash flows when detailed information on the exact timing of deaths is unavailable. Since the timing of death affects the present value of insurance benefits and premiums, the use of a uniform distribution assumption may influence the calculation of life insurance reserves. This study will examine the effect of the uniform distribution of deaths assumption on life insurance reserve estimates. It will assess how the assumption influences the valuation of future death benefits and determine the extent to which reserve estimates differ when deaths are assumed to occur uniformly compared with alternative timing assumptions. The study will also examine the sensitivity of reserve values to changes in the assumed distribution of deaths within policy years. The study will focus on the uniform distribution of deaths assumption, life insurance reserve estimates, mortality rates, death benefit valuation, actuarial present values, policy duration, life table functions, reserve valuation, premium payments, and mortality assumptions. Actuarial reserve models will be applied to estimate policy liabilities under the uniform distribution assumption. Alternative assumptions concerning the timing of deaths will also be considered to identify differences in projected reserve values. A quantitative research approach will be adopted for the study. Historical mortality and life table data will be analysed using descriptive statistics, actuarial valuation techniques, reserve calculation methods, comparative analysis, present value calculations, and sensitivity analysis. Life insurance reserves will be estimated using the uniform distribution of deaths assumption and compared with reserve estimates obtained under alternative assumptions about the timing of deaths. The study is expected to reveal that the uniform distribution of deaths assumption may have a measurable effect on life insurance reserve estimates. Assuming that deaths occur evenly throughout a policy year may produce reserve values that differ from those obtained under other mortality timing assumptions, particularly where interest rates, benefit amounts, or policy durations are substantial. The magnitude of the effect may depend on mortality rates, policy duration, interest rate assumptions, benefit structures, and the valuation method applied. The study will be useful to actuaries, life insurance companies, valuation analysts, underwriters, regulators, financial managers, and researchers. It may provide useful information for evaluating mortality timing assumptions, improving reserve calculations, assessing the sensitivity of life insurance liabilities, and strengthening actuarial valuation practices. The findings may also assist insurers in determining the appropriateness of the uniform distribution assumption for different classes of life insurance contracts. The study concludes that the uniform distribution of deaths assumption is an important consideration in life insurance reserve valuation because the assumed timing of mortality events can influence the present value of future benefit payments and resulting reserves. It is therefore recommended that insurers and actuaries carefully assess the suitability of the uniform distribution assumption, compare it with alternative mortality timing assumptions, and conduct sensitivity analysis to support accurate and consistent life insurance reserve estimates.

Keywords: Uniform distribution of deaths, life insurance reserve estimates, mortality assumptions, actuarial reserves, death benefit valuation, mortality rates, actuarial present values, life table functions, reserve valuation, policy duration, premium payments, mortality timing, interest rate assumptions, life insurance liabilities, actuarial analysis.