Insurance demand and welfare-maximizing risk capital—Some hints for the regulator in the case of exponential preferences and exponential claims

We propose two models to analyze welfare-maximizing capital requirements for insurance companies considering that capital is costly and therefore affecting the premium. Within a continuous-time model, we derive insurance demand and welfare as a function of personal wealth, the insurance company’s wealth, and the claims process, and compare them to their counterparts in a static model. Besides discussing welfare-maximizing capital, we provide some new insights on insurance demand.