The Economics of Adding and Subdividing Independent Risks: Some Comparative Statics Results.

Abstract

In this paper we address the problem of determining whether adding independent risks or subdividing them is a good substitute for insurance. Despite the fact that accepting more i.i.d. risks increases total risk, it is shown that some risk-averse decision makers can rationally reduce their demand for insurance by doing so. Similarly, a better diversified portfolio of i.i.d. risky assets can rationally be more insured, even if diversification is a risk-reduction scheme. We derive conditions sufficient to obtain unambiguous comparative statics results. Assuming that absolute risk aversion is decreasing and that the fourth derivative of the utility function is positive, we show that diversification is an exceptionally good substitute for insurance. Under the same conditions, adding independent risks to wealth reduces the demand for insurance on each unit. Copyright 1993 by Kluwer Academic Publishers