The number of people who receive a stable income for life from a closed pooled annuity fund is studied. Income stability is defined as keeping the income within a specified tolerance of the initial income in a fixed proportion of future scenarios. The focus is on quantifying the effect of the number of members, which drives the level of idiosyncratic longevity risk in the fund, on the income stability. To do this, investment returns are held constant, and systematic longevity risk is omitted. An analytical expression that closely approximates the number of fund members who receive a stable income is derived and is seen to be independent of the mortality model. An application of the result is to calculate the length of time for which the pooled annuity fund can provide the desired level of income stability.

研究了通过封闭式联合年金基金获得终身稳定收入的人数。收入稳定性的定义是在未来情况的固定比例下，使收入保持在初始收入的指定容限内。重点在于量化成员数量对收入稳定性的影响，这种影响推动了基金中特殊寿命风险的水平。为此，投资回报保持恒定，而系统的寿命风险则被忽略。得出了一个近似接近获得稳定收入的基金成员数量的分析表达式，并且该表达式与死亡率模型无关。结果的应用是计算合并年金基金可以提供所需水平的收入稳定性的时间长度。