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.

中文翻译：

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量化收入稳定性与池化年金基金成员数量之间的权衡

研究了从封闭式集合年金基金获得终生稳定收入的人数。收入稳定性被定义为在固定比例的未来情景中将收入保持在初始收入的指定容差范围内。重点是量化成员数量对收入稳定性的影响，这推动了基金中特殊长寿风险的水平。为此，投资回报保持不变，系统性长寿风险被忽略。推导出了一个非常接近获得稳定收入的基金成员数量的分析表达式，并且被视为独立于死亡率模型。该结果的一个应用是计算集合年金基金可以提供所需收入稳定水平的时间长度。