Tying life insurance and savings decisions: A multiperiod expected utility approach

Abstract

Many whole-life insurance contracts provide, in addition to protection in case of death of the insured, also a savings element. The main purpose of this article is to provide an economic rationale for this practice. Two alternative models are offered. In both models it is assumed that there is an asymmetry of information between the insurers and insureds, where the know better their probability of death, and hence adverse selection may cause a market failure. It is shown that by offering several deliberately designed contracts tying savings and insurance the insurers can induce the insureds to self select. That is, insureds with higher probability of death will voluntarily choose different contracts than those with a lower probability of death, and hence will reveal their probability of death to the insurers. The problem of adverse selection is thus overcome. In the first model contracts differ in the amount of insurance they specify and the amount of savings tied with insurance. In the second model a multiperiod (actually two period) contract and a single period contract are offered. The multiperiod contract specifies a savings element which will be received by the insured if he or she lives at the end of the second period. It is shown that by the right choice of the return on the savings part, insureds with lower probabilities of death will choose the multiperiod contract whereas insureds with higher probability of death will prefer two successive single period contracts. Again self selection is achieved. These two models show that tie-in arrangements of savings and insurance may help overcome the adverse selection problem, and hence an economic rationale is provided for their existence. The paper also examines the demand for life insurance and savings. The sensitivity of the demand for these products to variations in key parameters is analyzed. The differences between the sensitivity analyses results obtained when insurance and savings decisions are made separately and those obtained when these decisions are simultaneosly made are highlighted and explained.