A Mathematical Note on Inflation, Regulation, and the Cost of Life Insurance

Abstract

The influence of inflation on the cost of life insurance has received considerable attention.I While it is generally assumed that higher anticipated inflation is accompanied by a rationally perceived increasing real cost of life insurance protection (exceptions: Neumann [9] and Fortune [4]), a rigorous analytical treatment of the relationship has not been provided. Recently Babbel [1] identified an appropriate procedure for measuring inflation's impact on the cost of life insurance and then applied the technique to actual insurance policy data to demonstrate the potential magnitude of its impact [2]. Although a claim was made that under fixed insurance rates, anticipated inflation would raise the (rationally perceived) real cost of life insurance protection, no proof was presented. The purposes of this note are to present a rigorous proof of this claim, and to determine the extent to which premiums would need to be adjusted to leave the cost of life insurance unchanged. In this note, the net cost-benefit ratio suggested by Babbel will be used as a measure of the real cost'of life insurance. The effect of insurance rate regulation will be assumed to be one of maintaining at a fixed level the (nominal) terms stated in the policy (i.e., premiums, death benefit, and cash values, if any). The effect of expected inflation, therefore, will be limited to its impact upon the discount rate and upon any insurance values not specifically stipulated in the insurance contract (e.g., dividends). It is assumed that if prices are expected to rise, the discount rate will be higher, although not necessarily by the full amount of the anticipated inflation (i.e., dI/dj>O where I and j represent the discount factor and the expected rate of inflation, respectively.) The net cost-benefit ratio of a nonparticipating level premium term policy for an insured expecting to surrender his or her policy at the end of year k is given by