Premiums are Not Necessarily Monotonic with Interest and Age

Abstract

In a previous paper [Z1] we suggested to unify the study of changes in the force of mortality and the force of interest on life annuities, and we proposed estimates for the change in annuities, liabilities, premiums and reserves under change in the force of interest and the force of mortality.Dynamical life tables (DLT) use force of mortality that varies with time. Life insurance plans and pension schemes are recently considering DLT and variable rate of interest. Evaluation of annuities subject to DLT is quite complex. We suggested in [Z2] some approximations based on the estimates that we achieved in [Z1].In [Z3] we proved the conjecture that premium decreases when interest increases for whole life assurance for some ages, whenever the life table is of a standard population. In this paper we present a life table for which the conjecture is false, and we study the conjecture for the cases of term assurance and a pension scheme. We consider a similar conjecture that premium decreases when age increases, for some fixed interest.From the suggested life table we may deduce that the conjectures do not hold in all cases. The suggested life table is typical for a population that is subject to some high risk within a given range of ages, like young people being involved in car accidents, a risk that fades away with time and the survivors after the risky period are cured, healthy, and regular.