The Design of an Optimal Insurance Policy: Note

Abstract

In an article in this Review, Arthur Raviv (1979) examines Pareto optimal insurance policies when an insurer incurs settlement costs C induced by indemnity for loss x. Raviv's main result is that a necessary and sufficient condition for the Pareto optimal deductible to equal zero is C'(I) = 0. This implies that deductible policies give the best tradeoff between risk sharing and economizing on costly claim settlements. Since in practice these costs are significant, the theorem is of considerable importance. Among others, this has been recognized by Robert Townsend (1979), Michael Brennan and Ray Solanki (1981), David Mayers and Clifford Smith (1981), Gur Huberman, Mayers, and Smith (1983), Harris Schlesinger (1981), and Stuart Turnbull (1983). The theorem is correct, but Raviv's proof is not. In this note a corrected proof for the theorem is given. The corrected proof is important in itself because it allows for a generalization to a greater variety of transactions costs than has previously been considered (see my 1984 paper for details). Section I develops the setting for the problem and the notation to be subsequently used. Raviv's error and the corrected proof are presented in Section II.