On the optimal design of insurance contracts with guarantees

Abstract

Abstract The paper analyzes insurance contracts where the benefits of the insured depend on the performance of an investment strategy and which guarantee a certain interest rate on the contributions made by the insured. The insured has to decide simultaneously on the investment strategy and the guarantee scheme. For a CRRA insured and in a BS economy, the optimal combination is given by a constant mix strategy and the contribution guarantee scheme. In case the insured has a subsistence level, the CPPI strategy turns out to be optimal for arbitrary schemes. We illustrate our results by numerical examples and analyze the utility losses of a CRRA insured due to the use of a suboptimal combination of investment strategy and guarantee scheme.