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Effect of Actuarial Commutation Tables on Life Insurance Valuation

Abstract

Actuarial commutation tables are mathematical tools used to simplify life insurance calculations by providing values derived from mortality and interest rate functions. They contain functions such as DxD_x, NxN_x, CxC_x, and MxM_x, which enable actuaries to calculate premiums, reserves, annuity values, and other life insurance quantities efficiently. The use of commutation tables can therefore influence the accuracy and efficiency of life insurance valuation, particularly when evaluating contracts with complex benefit and premium structures. This study will examine the effect of actuarial commutation tables on life insurance valuation. It will assess how commutation functions influence the calculation of actuarial present values of premiums and benefits and the resulting values of life insurance contracts. The study will also examine how changes in mortality assumptions, interest rates, age at entry, and policy duration affect valuation results obtained using commutation table functions. The study will focus on actuarial commutation tables, life insurance valuation, commutation functions, mortality rates, survival probabilities, actuarial present values, life insurance premiums, policy reserves, policy duration, age at entry, and interest rate assumptions. Selected commutation functions will be applied to calculate the values of different life insurance benefits and premium streams. The study will examine the relationship between the underlying mortality and interest assumptions and the resulting commutation values used in actuarial calculations. A quantitative actuarial research approach will be adopted for the study. Mortality data and interest rate assumptions will be used to construct relevant commutation functions for selected ages and policy durations. Actuarial present value calculations, commutation table techniques, comparative analysis, sensitivity analysis, and mathematical modelling will be employed to determine life insurance values. The resulting estimates may also be compared with direct actuarial calculations to assess differences in valuation outcomes. The study is expected to reveal that actuarial commutation tables may have a significant effect on life insurance valuation by providing a structured basis for calculating the present values of future premiums and benefits. Variations in mortality and interest rate assumptions are expected to produce corresponding changes in commutation functions and life insurance values. The magnitude of the effect may depend on age at entry, policy duration, benefit structure, premium payment pattern, mortality experience, and the assumed interest rate. The study will be useful to actuaries, life insurance companies, pricing analysts, valuation specialists, underwriters, regulators, and actuarial science researchers. It may provide useful information on the application of commutation tables in life insurance valuation and assist practitioners in understanding how mortality and interest assumptions affect the values generated by commutation functions. The findings may also support efficient actuarial calculations and improve the interpretation of life insurance valuation results. The study concludes that actuarial commutation tables are important tools in life insurance valuation because they provide an efficient mathematical framework for calculating the present values of premiums and benefits. It is therefore recommended that insurers and actuarial practitioners ensure that commutation tables are constructed from appropriate mortality and interest assumptions, regularly reviewed, and applied consistently when valuing life insurance contracts.

Keywords: Actuarial commutation tables, life insurance valuation, commutation functions, mortality rates, survival probabilities, actuarial present value, life insurance premiums, policy reserves, mortality assumptions, interest rate assumptions, age at entry, policy duration, actuarial calculations, insurance benefits, actuarial modelling.