Cross-subsidizing effects between existing and new policyholders in traditional life insurance

For many life insurance companies, traditional life insurance with surplus participation is still a major portion of their business. As a consequence of the low interest rate environment, financial guarantees of new contracts have been decreased. Hence, new business reduces the average guaranteed rate of interest for the whole block of business. At the same time, however, new policyholders benefit from higher yields of assets in the existing asset portfolio built up with previous policyholders' contributions. Therefore, it is not obvious whether new policyholders benefit from or subsidize the existing portfolio. In this paper, we use the collective bonus introduced in Eckert et al. (Eur Actuar J, 2020) to measure the interaction between new policyholders and the existing insurance portfolio. Considering the situation in Germany as an example, we measure and explain cross-subsidizing effects resulting from different cohorts of policyholders being linked to the same asset portfolio. In particular, we show under which circumstances there is a benefit for or subsidization from new business.