Insurance and Consumption: The Continuous Time Case

Abstract

During the last twenty years, a large body of literature devoted to the determination of the optimal insurance coverage has developed. The seminal works by Arrow (1963), Smith (1968) and Mossin (1968) provide the corner stone results of insurance economics. But surprisingly enough this literature only concentrated on the case of a single insurable asset, thus implicitly assuming a perfect separability of the insurance decision. Recent research has shown that this picture must be modified when insurance demand is jointly analyzed with portfolio or consumption decisions. In the portfolio case, insurance coexists with background risk. The optimal level of insurance coverage is affected by covariance effects between the potential loss and the socalled background risk. (see e.g. Doherty and Schlesinger [1983, Mayers and Smith (1983)1). The consumption case has been less intensively examined. As recently noted by Dionne and Eeckhoudt (1984) 'the literature on the demand for damage insurance and that on optimal saving seem to have followed rather independent paths. Moffet (1977), Falciglia (1980) and Dionne and Eeckhoudt (1984) have derived some propositions about the possible interactions between consumption and insurance decisions but their works constitute notable exceptions to the general course of research in optimal insurance. The specific purpose of this note is to extend the three last mentioned contributions and more precisely to analyze the consumption and insurance decisions in a continuous time setting using the methods of Merton (1969). Sufficient conditions for a separability of the insurance decision will be given. Separability means that decisions can be made sequentially without any feed back on each other.