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Effect of Balducci Mortality Assumption on Life Insurance Premium Estimates

Abstract

The Balducci mortality assumption is an actuarial method used to estimate mortality probabilities within fractional age intervals when mortality information is available at integer ages. The assumption provides a basis for interpolating survival and death probabilities between successive ages and is therefore relevant to actuarial calculations involving life insurance premiums. Since mortality assumptions influence the probability and timing of future benefit payments, the choice of mortality interpolation method may affect the estimated premium required for life insurance contracts. This study will examine the effect of the Balducci mortality assumption on life insurance premium estimates. It will assess how the assumption influences mortality probabilities, survival probabilities, expected insurance benefits, and the actuarial present values used in determining life insurance premiums. The study will also examine variations in premium estimates resulting from the application of the Balducci assumption under different ages, policy durations, benefit structures, and interest rate assumptions. The study will focus on the Balducci mortality assumption, mortality interpolation, fractional age probabilities, survival probabilities, life insurance premiums, actuarial present values, mortality tables, policy duration, age at entry, and interest rates. Actuarial life table functions will be applied to estimate the probabilities of death and survival between integer ages. Net premium calculations will then be performed to determine how the resulting mortality estimates influence the premium required for selected life insurance contracts. A quantitative actuarial research approach will be adopted for the study. Mortality data obtained from standard life tables will be used to construct mortality and survival probabilities under the Balducci assumption. Actuarial present value techniques, life table functions, comparative analysis, sensitivity analysis, and mathematical modelling will be employed to estimate premiums under different assumptions. The resulting premium estimates may also be compared with estimates obtained using alternative mortality interpolation assumptions to assess the extent of variation. The study is expected to reveal that the Balducci mortality assumption may have a measurable effect on life insurance premium estimates, particularly for policies involving fractional ages, short policy durations, or benefits that are sensitive to the timing of mortality. Differences in mortality interpolation may produce variations in expected benefit payments and actuarial present values, thereby influencing the premiums estimated for life insurance contracts. The magnitude of the effect is expected to depend on the mortality table, age at entry, policy term, benefit amount, and interest rate assumptions. The study will be useful to actuaries, life insurance companies, pricing analysts, underwriters, valuation specialists, regulators, and actuarial science researchers. It may provide useful information on the application of the Balducci assumption in life insurance premium estimation and help practitioners understand how mortality interpolation choices can affect actuarial calculations. The findings may also support more informed selection of mortality assumptions when estimating premiums for different life insurance products. The study concludes that the Balducci mortality assumption is an important actuarial interpolation approach that can influence life insurance premium estimates through its effect on fractional-age mortality and survival probabilities. It is therefore recommended that insurers and actuarial practitioners carefully evaluate the suitability of the Balducci assumption for the mortality data and insurance products under consideration and assess the sensitivity of premium estimates to alternative mortality assumptions.

Keywords: Balducci mortality assumption, life insurance premiums, mortality interpolation, fractional age, mortality probabilities, survival probabilities, actuarial present value, mortality tables, life insurance valuation, actuarial modelling, net premiums, policy duration, age at entry, interest rate assumptions, mortality assumptions.