Risk- and Value-Based Management for Non-Life Insurers Under Solvency Constraints

Abstract

The aim of this paper is to propose an internal model for a non-life insurer and to apply this model for deriving optimal risk- and value-based management decisions regarding the insurer’s investment strategy, which contribute to increasing shareholder value. We thereby considerably extend previous work by explicitly accounting for the policyholders’ willingness to pay depending on their risk sensitivity based on the insurer’s reported solvency status, which will be of great relevance under Solvency II. We further study the impact of the risk-free interest rate on attainable and admissible risk-return asset combinations, dependencies between assets and liabilities as well as the influence of reinsurance contracts, and we derive analytical solutions for maximizing shareholder value. One main finding is that the consideration of the policyholders’ willingness to pay depending on their risk sensitivity towards the insurer’s reported solvency status is vital for optimal management decisions and that in the present setting, reinsurance increases shareholder value only for non-risk sensitive policyholders. Our results further emphasize that low interest rates strongly restrict the insurer’s investment opportunities.