The Pareto-optimal Design of Term Life Insurance Contracts

Numerous investigations have been directed toward aspects of rational life insurance purch&es and optimal coverage levels under differing conditions. Most of these studies have taken as "given" the design of life insurance contracts and have focused on optimal consumer responses to available insurance opportunities.' However, in works by Borch (1960, 1983), Arrow (1963, 1974) and Raviv (1979), contract design has been considered explicitly, yet in none of these studies has the focus been on life insurance; rather, general property and liability insurance received attention. The present study focuses on the design of life insurance contracts. In it results are derived from first principles for the case of life insurance that have their analogues in the work of Arrow on general insurance. Aspects of the life insurance problem that diverge from other insurance problems lead to an optimal policy design that may differ from those appropriate for other lines of i n ~ u r a n c e . ~ The simplicity of the lottery associated with life insurance allows us to describe consumers' coverage as a function of premium, facilitating a direct examination of alternative rate structures. This is in contrast to traditional approaches wherein optimality is described through relations of final wealth in different states of the world. We show, under very general conditions, how life insurance contracts can be designed so as to lead to increases in the welfare of insurance consumers, companies, and sales persons (i.e., insurance agents). Unlike other studies, which indicate that less than full coverage is optimal when a positive loading factor is incorporated into insurance rates, we show that full coverage is quite plausible under a positive loading factor, provided that the load is incorporated into insurance rates according to the manner herein specified. Another new result of this paper is that insurance consumers will desire h~gher