INSURANCE AND PRECAUTIONARY CAPITAL ACCUMULATION IN A CONTINUOUS-TIMEMODEL

This article analyzes the optimal dynamic strategy of a risk-averse ag ent bearing an insurable risk to determine whether precautionary savin g is superior to insurance in the long run. The risk of loss is descri bed 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 vanish es in the long run if the loading factor exceeds a.critical value whic h is strictly positive. However, insurance may be a transitory strateg y to protect capital accumulation. The optimal strategy for capital ac cumulation and insurance demand is derived in the constant relative ri sk aversion case. It is also shown that compulsory full insurance redu ces the rate of consumption if and only if risk aversion exceeds one.