INSURANCE AND PRECAUTIONARY CAPITAL ACCUMULATION IN A CONTINUOUS-TIME MODEL

This article analyzes the optimal dynamic strategy of a risk-averse agent bearing an insurable risk to determine whether precautionary saving is superior to insurance in the long run. The risk of loss is described by a Poisson process. Policyholders can purchase insurance and/or accumulate precautionary savings in order to forearm themselves in the face of uncertainty. It is shown that the demand for insurance vanishes in the long run if the loading factor exceeds a.critical value which is strictly positive. However, insurance may be a transitory strategy to protect capital accumulation. The optimal strategy for capital accumulation and insurance demand is derived in the constant relative risk aversion case. It is also shown that compulsory full insurance reduces the rate of consumption if and only if risk aversion exceeds one.