Scand. Actuarial J. 1985: 4963
The Pareto-optimal Design of Term Life
Insurance Contracts
By David F. Babbel and Nicholas S. Economides
I. Introduction
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 explicit-
ly, 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 in~urance.~
The simplicity of the lottery associated with life insur-
ance 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 incorpo-
rated into insurance rates according to the manner herein specified. Anot