A Novel Analytical Technique of Estimating Whole Life Insurance Benefits Payable Multiple Times Per Period of Insurance

Abstract

The deepest form of actuarial estimation problems remains the subject of classical life insurance
methodologies. A life insurance contract provides the payment of a defined sum assured contingent
upon the death of an insured life. Although in practice, death benefits is payable as soon as death
claim is advised and the legal requirement is completed, it is necessary to examine death benefits
which are paid at the end of policy anniversary of death, that is on the first policy anniversary of
effecting the policy after death. When the frequency of payments of an mthly life insurance benefit
scheme is infinite, the resulting life insurance function becomes continuously payable momentarily
throughout the year so that the total annual payment is equivalent to 1. This admittedly artificial
phenomenon has marked consequences in classical life contingency applications and at the same
time important as an estimation of benefits payments made weekly or monthly in life insurance
benefit program. Consequently, the approximation in the form most suitable for this purpose will
be based on Bernoulli power series. In this paper, the objective is to construct analytical
expressions for whole life insurance functions payable at different frequencies where the resulting
expression represents an adjustment to the yearly formula. Unless an analytical expression for the
survival function at age x is defined, approximation will be required to evaluate this expressions.
From the results obtained, we confirm asymptotically that ( )
lim K
x
K
→
x
=
A A
.