Life Insurance Purchasing to Maximize Utility of Household Consumption

TL;DR

This paper derives the optimal life insurance amount for a household with two wage earners using exponential utility, showing equivalence in consumption and loss probabilities under different premium schemes.

Contribution

It explicitly determines the optimal death benefit for both single premium and continuous premium schemes in a simplified utility framework.

Findings

Optimal death benefits are explicitly derived.

Consumption rates are identical under different premium schemes.

Loss probabilities are equivalent for households and insurers.

Abstract

We determine the optimal amount of life insurance for a household of two wage earners. We consider the simple case of exponential utility, thereby removing wealth as a factor in buying life insurance, while retaining the relationship among life insurance, income, and the probability of dying and thus losing that income. For insurance purchased via a single premium or premium payable continuously, we explicitly determine the optimal death benefit. We show that if the premium is determined to target a specific probability of loss per policy, then the rates of consumption are identical under single premium or continuously payable premium. Thus, not only is equivalence of consumption achieved for the households under the two premium schemes, it is also obtained for the insurance company in the sense of equivalence of loss probabilities.