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Effect of Last-Survivor Probabilities on Joint-Life Annuity Valuation

Abstract

Joint-life annuities are actuarial contracts that provide periodic payments based on the survival of two or more individuals. In a last-survivor annuity, payments continue until the death of the last surviving individual covered by the contract. The probability that at least one of the lives remains alive at a given time is therefore an important component of actuarial valuation and directly influences the expected duration and present value of annuity payments. This study examines the effect of last-survivor probabilities on joint-life annuity valuation. It will investigate how variations in the probability of at least one member of a joint-life group surviving to future periods affect the actuarial present value of annuity benefits. The study will consider the relationship between last-survivor probabilities, expected payment duration, and the resulting value of joint-life annuity contracts. The study will focus on important actuarial factors including the ages of the lives covered, mortality rates, survival probabilities, interest rate assumptions, and annuity payment periods. Appropriate joint-life and last-survivor actuarial functions will be applied to determine how changes in these factors influence the valuation of annuity benefits. Differences in survival patterns between the covered lives will also be considered in assessing the expected continuation of payments. A quantitative research approach will be adopted for the study. Relevant mortality and life table data will be used to estimate joint-life and last-survivor probabilities under different actuarial assumptions. Actuarial present value calculations, descriptive analysis, and comparative valuation techniques will be employed to examine changes in annuity values resulting from variations in last-survivor probabilities and other valuation parameters. The study is expected to show that higher last-survivor probabilities may result in longer expected payment periods and consequently higher actuarial present values for joint-life annuities. Conversely, lower survival probabilities may shorten the expected duration of payments and reduce their present values. The study may also reveal that differences in age combinations, mortality experience, and interest rate assumptions can produce noticeable variations in the valuation of last-survivor annuity benefits. The study is expected to provide useful information for actuaries, insurance companies, pension administrators, and financial institutions involved in annuity valuation and product design. A clearer understanding of last-survivor probabilities can improve the estimation of future benefit obligations and support more accurate pricing, reserve assessment, and financial planning for joint-life annuity contracts. The study concludes that last-survivor probabilities constitute an important component of joint-life annuity valuation because they determine the likelihood and expected duration of continued benefit payments. It is therefore recommended that actuaries incorporate appropriate mortality data, survival assumptions, interest rates, and joint-life valuation techniques when determining the actuarial present value of last-survivor annuities. This can promote more reliable valuation and better management of long-term annuity obligations.

Keywords: Last-survivor probabilities, joint-life annuity, annuity valuation, actuarial present value, survival probabilities, mortality rates, joint-life status, last-survivor status, life tables, annuity benefits, interest rates, payment duration, actuarial functions, mortality assumptions, insurance valuation.