Research On The Interpolation Of Life Table Functions In Life Contingencies

Actuarial Science is a fairly unique blend of mathematics, economics, and real world business understanding, all designed to give an understanding of sound practical ways in which financial risk of insurance companies and pension funds can be managed.In life contingencies, the assumption on life table function is an elementary problem. Since one only knows the values of survival function in some points of age, to calculate the probabilities of death for fractions of a year, the commonly strategy is making some assumptions regarding the pattern of the probabilities of the death.Under the three conventional assumptions, the interpolated values of the survival function between two consecutive ages depend only on the survival function at those ages. While this has the advantage of simplicity, all three assumptions result in force of mortality and probability density functions with implausible discontinuities at integer ages. Therefore, we want to find a fractional age assumptions to get a more reasonable force of mortality function and more accurate actuarial present values.In this paper, the force of mortality function and the density function of future lifetime are assumed in a 6-degree polynomial form. A generalized integral interpolation method is used to get the value of life table functions at any age interval from the survival value in life table. The premium under this assumption is calculated and compared with the premium under conventional assumption.The paper is organized into five chapters. Chapter One gives the background, structure and innovation of the whole paper. Chapter Two makes a review of related studies on the form of life table functions. Chapter Three introduces the familiar life table functions in life contingencies, the three conventional assumptions on fractional age, and the calculation of life insurance premium and present value of annuities, conventional interpolation method and a generalized integral interpolation method which is used in this paper. Chapter Four compares different interpolation methods and assumptions, and shows the optimal form of life table functions.