Optimal Purchasing of Deferred Income Annuities When Payout Yields are Mean-Reverting
Optimal Purchasing of Deferred Income Annuities When Payout Yields are Mean-Reverting
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当支付收益率均值回归时递延收入年金的最佳购买
DOI：
10.2139/ssrn.2580420
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
V. Young
中科院分区：
文献类型：
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作者：
Huaxiong Huang;M. Milevsky;V. Young
我们确定的最佳生命周期购买策略递延收入年金（DIA）-这是不同于单一保费收入年金（SPIA）-个人谁希望最大化他/她的年金收入在未来的一个固定时间的预期效用。与SPIA的大量投资组合选择文献相反，我们专注于DIA支出收益率的随机性，并解决了人们对利率目前“太低”而无法证明不可逆年化的担忧。我们假设一个均值回归模型的支付收益率，并表明，风险中性的消费者希望最大限度地提高他/她的预期退休收入应该等到收益率达到一个阈值，这是高于历史平均水平，然后购买DIA一次性。相比之下，一个风险厌恶的消费者担心支付收益率将保持低于平均水平的一段时间，并担心失去死亡率信用，而等待，应采用障碍购买策略，在交易成本下的投资组合选择问题。我们说明了如何将这一见解应用于年金化的背景下。事实上，风险厌恶型消费者的最佳行为类似于非对称的美元成本平均策略，即使支出率低于历史平均水平，也会花费一部分DIA预算。作为我们分析的一部分，我们提供了一个易于使用的最佳购买策略（阈值）的渐近近似，并提供了一些数值例子来说明这个概念。
We determine the optimal lifecycle purchasing strategy for deferred income annuities (DIAs)—which are distinct from single-premium income annuities (SPIAs)—for an individual who wishes to maximize the expected utility of his/her annuity income at a fixed time in the future. In contrast to the vast portfolio-choice literature for SPIAs, we focus on the stochasticity of the DIA’s payout yield and address concerns that rates are currently “too low” to justify irreversible annuitization. We assume a mean-reverting model for payout yields and show that a risk-neutral consumer who wishes to maximize his/her expected retirement income should wait until yields reach a threshold—which lies above historical averages—and then purchase the DIA in one lump sum. In contrast, a risk-averse consumer who is concerned the payout yield will remain below average for an extended period and worries about losing mortality credits while waiting, should employ a barrier purchasing strategy, as in the portfolio choice problem under transaction costs. We illustrate how this insight is applied in the context of annuitization. In fact, the optimal behavior of a risk-averse consumer resembles an asymmetric dollar-cost averaging strategy, with a portion of the DIA-budget spent even while payout rates are below historical averages. As part of our analysis we offer an easy-to-use asymptotic approximation for the optimal purchasing strategy (threshold) and provide some numerical examples to illustrate the concept.