Analytical Representation Technique of Modelling Present Value Function and the Application to Life Table Functions under the Framework of Chebyshev Polynomial

Abstract

In life insurance analysis, weighing insured’s benefits and contributions which occur over time requires discounting those amounts to present value equivalents. Therefore, the choice of discount rate can be consequential for the valuation of insurance policies. Out of the functions making up the life insurance products, there seems to be no closed form numerical estimates for the interest rate intensity and present value functions. This identified problem may either be in favour of the insured or ortherwise. However, the practice favours the life insurer most in actuarial valuation under the deterministic parsimonious setting. Empirical evidence suggests that new theoretical model advances given the future uncertainty likely suggesting lower long-term rates. This evidence generally supports lowering discount rates under a feasible best guess based on the available financial information. This necessitates deriving a discount rate which can adjust for the fact that benefits are more valuable at present than in the future if policyholders prefer to buy cover now rather than wait or if insurers could be earning a positive return on invested incomes. In this study, the objectives is to develop model for the present value function under the Chebyshev polynomial series framework within the interval of orthogonality and then define some life table structures on the model. From our analytical constructions, as the argument of the polynomial series tends to, we obtain the present value function, which attempts to balance the interests of the policyholders and the life insurers.