The Simple Analytics of a Pooled Annuity Fund
The Simple Analytics of a Pooled Annuity Fund
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DOI：
10.1111/j.1539-6975.2005.00134.x
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发表时间：
2005-08
期刊：
影响因子：
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通讯作者：
J. Piggott;Emiliano A. Valdez;B. Detzel
中科院分区：
文献类型：
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作者：
J. Piggott;Emiliano A. Valdez;B. Detzel
本文提供了长寿风险汇集基金支付调整的正式分析，这种安排我们称为集团自我年化(GSA)。在长寿保险工具家族中，GSA的显著风险扩散特征是年金人承担其系统性风险，而年金池则分担特殊风险。这消除了对保险公司的需要，尽管此类工具可以通过公司保险公司销售。我们首先推导出具有单一年金系数和恒定预期的单个入职组的支出调整。然后，我们证明了在弱需求下，当多个队列合并到一个池中时，存在支付路径的唯一解决方案。这依赖于各队列的已实现存活率与预期存活率之比的调和平均值。本文还分析了演化预期的情形。在所有情况下，我们都证明，集合年金基金中的定期福利付款是根据先前的付款确定的，该付款根据死亡率和利息与预期的任何偏差进行了调整。在采用国家固定缴费计划和/或人寿保险业缺乏竞争力或欠发达的国家，GSA可能具有相当大的吸引力。
This article provides a formal analysis of payout adjustments from a longevity risk-pooling fund, an arrangement we refer to as group self-annuitization (GSA). The distinguishing risk diffusion characteristic of GSAs in the family of longevity insurance instruments is that the annuitants bear their systematic risk, but the pool shares idiosyncratic risk. This obviates the need for an insurance company, although such instruments could be sold through a corporate insurer. We begin by deriving the payout adjustment for a single entry group with a single annuity factor and constant expectations. We then show that under weak requirements a unique solution to payout paths exists when multiple cohorts combine into a single pool. This relies on the harmonic mean of the ratio of realized to expected survivorship rates across cohorts. The case of evolving expectations is also analyzed. In all cases, we demonstrate that the periodic-benefit payment in a pooled annuity fund is determined based on the previous payment adjusted for any deviations in mortality and interest from expectations. GSA may have considerable appeal in countries which have adopted national defined contribution schemes and/or in which the life insurance industry is noncompetitive or poorly developed.