Equivalence principle and Jewell’s inequality

In his address to the 21st International Congress of Actuaries, the late Professor William S. Jewell pointed out that, for a whole life insurance policy with level premiums payable continuously and a death benefit of constant amount payable at the moment of death, even though the equivalence principle stipulates that the insurer’s expected gain at issue is zero, the insurer’s expected gain at the moment of death of the insured is positive. This seemingly surprising result turns out to be true for more general life insurance policies. We present a simple derivation of and some elaboration on this fact.