Optimal insurance coverage in situations of pure and speculative risk and the risk-free asset

The insured's portfolio consists of an insurable (pure) risk, an uninsurable (speculative) risk, a (proportional) insurance policy and a risk-free asset. The optimal insurance policy (i.e., the proportion to be insured) is examined from the insured's point of view, using the reward to variability concept. The importance of the risk-free asset in reaching an exact and explicit solution is analyzed, while emphasizing the possibility of substitution of the risk-free investment and insurance mechanisms. The paper demonstrates possibilities of improving the insured's welfare by the use of the risk-free rate - which is sometimes less expensive than other risk reduction instruments. The analysis leads to a two-step solution, similar to the well- known Hirschleifer investment model and to the famous Capital Assets Pricing Model.