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Effect of Ultimate Life Table Functions on Annuity Valuation

Abstract

Ultimate life table functions provide actuarial measures of mortality and survival after the effects associated with the select period have ended. They are used to represent mortality experience at different ages and form an important basis for estimating the duration and probability of future life-contingent payments. In annuity valuation, appropriate ultimate life table functions are important because the expected present value of annuity benefits depends on the probability that payments will continue while the annuitant remains alive. This study will examine the effect of ultimate life table functions on annuity valuation. It will assess how variations in ultimate mortality and survival functions influence the actuarial present value of life annuity benefits. The study will also compare annuity values calculated under different ultimate life table assumptions to determine the extent to which changes in mortality functions affect actuarial valuation results. The study will focus on ultimate life table functions, annuity valuation, mortality rates, survival probabilities, life expectancy, actuarial present values, life annuity payments, interest rates, discount factors, mortality assumptions, annuity factors, payment duration, and actuarial valuation. Life table functions will be applied to estimate expected survival and mortality patterns and determine their implications for the valuation of future annuity payments. A quantitative research approach will be adopted for the study. Relevant age-specific mortality rates, survival probabilities, annuity payment amounts, interest rates, payment frequencies, and contract durations will be analysed using actuarial valuation techniques. Descriptive analysis, comparative analysis, actuarial present value calculations, sensitivity analysis, and mathematical modelling will be used to evaluate differences in annuity values under alternative ultimate life table functions. The study is expected to reveal that ultimate life table functions may have a significant effect on annuity valuation. Mortality assumptions indicating longer survival are expected to increase the expected duration of annuity payments and may consequently increase actuarial present values, while higher mortality assumptions may produce lower expected values. The magnitude of the effect may depend on the annuitant's age, mortality experience, interest rates, payment frequency, benefit amount, and contract duration. The study will be useful to actuaries, insurance companies, annuity providers, pension administrators, retirement fund managers, financial planners, regulators, researchers, and students of actuarial science. It may provide useful information for selecting appropriate mortality assumptions, improving annuity valuation accuracy, designing retirement income products, estimating insurer liabilities, and assessing the financial implications of changes in mortality experience. The study concludes that ultimate life table functions are important considerations in annuity valuation because mortality and survival assumptions directly influence the expected duration and present value of future annuity payments. It is therefore recommended that actuaries and annuity providers regularly evaluate the suitability of ultimate life table functions and incorporate appropriate mortality assumptions when valuing life annuity contracts.

Keywords: Ultimate life table functions, annuity valuation, ultimate mortality, mortality rates, survival probabilities, life expectancy, actuarial present values, life annuity payments, interest rates, discount factors, mortality assumptions, annuity factors, payment duration, actuarial valuation, annuity contracts.