Optimal Investment and Premium Policies under Risk Shifting and Solvency Regulation

Risk shifting is a well-known agency problem in corporate finance which also exists between policyholders and shareholders of insurance companies. Shareholders engage in excessive risk taking at the expense of policyholders who, in turn, are less willing to pay for insurance coverage. Solvency regulation addresses this incentive problem by restricting the set of investment strategies and premium policies. We first characterize Pareto optimal investment and premium policies and provide necessary and sufficient conditions for their existence and uniqueness. We then show that if shareholders cannot credibly commit to an investment strategy before policies are sold, they pursue an investment strategy that is either most risky or not risky at all. Last, we specify the conditions under which solvency regulation, such as Solvency II or the Swiss Solvency Test, mitigates the inefficiency of the risk shifting problem.