Analyzing surplus appropriation schemes in participating life insurance from the insurer’s and the policyholder’s perspective

This paper examines the impact of three surplus appropriation schemes often inherent in participating life insurance contracts on the insurer’s shortfall risk and the net present value from an insured’s viewpoint. (1) In case of the bonus system, surplus is used to increase the guaranteed death and survival benefit, leading to higher reserves; (2) the interest-bearing accumulation increases only the survival benefit by accumulating the surplus on a separate account; and (3) surplus can also be used to shorten the contract term, which results in an earlier payment of the survival benefit and a reduced sum of premium payments. The pool of participating life insurance contracts with death and survival benefit is modeled actuarially with annual premium payments; mortality rates are generated based on an extension of the Lee-Carter (1992) model, and the asset process follows a geometric Brownian motion. In a simulation analysis, we then compare the influence of different asset portfolios and shocks to mortality on the insurer’s risk situation and the policyholder’s net present value for the three surplus schemes. Our findings demonstrate that, even though the surplus distribution and thus the amount of surplus is calculated the same way, the type of surplus appropriation scheme has a substantial impact on the insurer’s risk exposure and the policyholder’s net present value.