Optimal Investment and Premium Policies under Risk Shifting and Solvency Regulation

TL;DR

This paper characterizes optimal investment and premium policies for insurance companies considering risk shifting incentives and solvency regulation, highlighting conditions for their existence and the impact of regulatory frameworks.

Contribution

It provides a theoretical framework for Pareto optimal policies under risk shifting and analyzes how solvency regulation affects agency costs in insurance.

Findings

Existence and uniqueness conditions for optimal policies.

Risk shifting incentives influence policy design.

Solvency regulation reduces agency costs.

Abstract

Limited liability creates a conflict of interests between policyholders and shareholders of insurance companies. It provides shareholders with incentives to increase the risk of the insurer's assets and liabilities which, in turn, might reduce the value policyholders attach to and premiums they are willing to pay for insurance coverage. We characterize Pareto optimal investment and premium policies in this context and provide necessary and sufficient conditions for their existence and uniqueness. We then identify investment and premium policies under the risk shifting problem if shareholders cannot credibly commit to an investment strategy before policies are sold and premiums are paid. Last, we analyze the effect of solvency regulation, such as Solvency II or the Swiss Solvency Test, on the agency cost of the risk shifting problem and calibrate our model to a non-life insurer average portfolio.