The Gradshteyn and Ryzhik’s Integral and the Theoretical Computation of involving the Continuous Whole Life Annuities

Abstract

Abstract: Considering the risk connected with the expectation of life at retirement as a result of the unavailable actuarially modeled life annuity to price life insurance products, this study explores the gains in an annuity that would be advantageous to lives who choose life annuity option at retirement under defined condition of actuarially fair annuity value. When continuous parsimonious parametric mortality intensities are Makehamised, then the life table functions used in computing the actuarial present values of the fully continuous whole life insurance and the fully continuous life annuity could be expressed in terms of special functions such as Gamma, Incomplete lower Gamma and Incomplete upper Gamma functions for a homogeneous insured population. In this study, the objective is to

(i) Construct mathematical estimations through single life parameterization through algebraic technique (ii) Apply the mean value theorem to construct modification theorems under the framework of policy alterations

(iii) Employ the properties of the aforementioned special functions to construct estimations which could permit us to compute closed-form expressions for continuous whole life insurance and continuous whole life expectancy applicable in classical life contingencies.

(iv) Apply the commutation function to develop a mathematical model for the employer liability. From our results, Gradshteyn and Ryzhik's analytic integral technique presents an advanced technique for computing life insurance biometric functions and ignores the need for any algorithmic numerical procedures.

Keywords: GM (1,2), Whole life insurance, whole life annuity, Gradshteyn and Ryzhik's integral, Gamma functions