S. Spaeter et P. Roger, THE DESIGN OF OPTIMAL INSURANCE CONTRACTS - A TOPOLOGICAL APPROACH, Geneva papers on risk and insurance. Theory, 22(1), 1997, pp. 5-19
This article deals with the optimal design of insurance contracts when
the insurer faces administrative costs. If the literature provides ma
ny analyses of risk sharing with such costs, it is often assumed that
these costs are linear. Furthermore, mathematical tools or initial con
ditions differ from one paper to another. We propose here a unified fr
amework in which the problem is presented and solved as an infinite di
mensional optimization program on a functional vector space equipped w
ith an original norm. This general approach leads to the optimality of
contracts lying on the frontier of the indemnity functions set. This
frontier includes, in particular, contracts with a deductible, with to
tal insurance and the null vector. Hence, we unify the existing result
s and point out some extensions.