This paper analyzes lifetime pension payouts under the German statutory system using continuous Gompertz mortality models. We compare pay-as-you-go benefits with a scenario in which contributions are invested in the capital market, yielding a benchmark capital stock of approximately €604,000 over a 45-year career. We derive the full distribution of individual pension payouts, including expected values and quantiles, and extend traditional life-table calculations to a continuous-time framework. Present-value distributions account for differences between pension growth rates and discount rates, and a sensitivity analysis quantifies the impact of key Gompertz parameters on both expected payouts and their dispersion. Results indicate that higher discount rates reduce present values and tighten payout distributions, while higher pension growth increases risk due to heavier tails. The framework provides a transparent, extendable method for evaluating pension schemes, assessing demographic and financial risks, and supporting actuarial decision-making.
Jöckel et al. (Fri,) studied this question.