Optimal insurance design in the presence of government financial assistance

This paper revisits the study of insurance demand in the context of potential government financial assistance, such as ex post disaster relief and ex ante premium subsidies. We impose the incentive-compatibility condition on the indemnity, and assume that the premium is determined by the actuarial-value-based premium principle. By applying Ohlin's lemma, we characterize the optimal forms of the indemnity function under independence between the relief event and the insurable loss. The optimal parameters of the indemnity function are derived, and both analytical and numerical comparative studies are conducted to demonstrate the effects of disaster relief and premium subsidies on the demand for insurance. Furthermore, we study two forms of dependence between the relief event and the insurable loss. First, we study one specific yet common loss-dependent relief probability case. Second, we study special cases of conditional insurable loss distributions using the hazard rate ordering. Also, we study the effect of premium subsidies on the insurance demand, and show that premium subsidies increase the demand for insurance under increasing absolute risk aversion. The results provide new insights into the study of natural hazard insurance demand in the presence of government interventions.