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首页> 外文期刊>Journal of pension economics and finance >Optimal consumption and portfolio choice of retirees with longevity risk
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Optimal consumption and portfolio choice of retirees with longevity risk

机译：具有长寿风险的退休人员的最优消费和投资组合选择

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摘要

The question how to optimize consumption and portfolio choice over the life cycle has been widely discussed in the literature so far. In this paper we concentrate on a retiree's optimal consumption and portfolio selection over his remaining years of life. We apply the logistic model of mortality thus modeling the empirically observed increase of mortality during the retirement period. The optimal consumption strategy and portfolio choice are established by reducing the Hamilton-Jacobi-Bellmann equation to the explicit solution of an ordinary differential function (ODF) that includes the mortality rate. A general finding is that the Merton-Samuelson result of constant portfolio choice for a constant mortality is confirmed for arbitrary mortality. The portfolio choice is only influenced by risk and return of assets and the retirees' risk aversion. To get the specific optimal consumption strategy in a realistic situation the logistic model of mortality has been fitted to the data of the Statistical Yearbook for the Federal Republic of Germany 2006/2008. The optimal initial value for the ODF is obtained by numerical methods. The solution provides a large increase in the ratio of optimal consumption to wealth up to about 92 years followed by a sharp decrease. A bequest motive dampens the magnitudes of the ups and downs of the consumption ratio but does not change the basic shape.
机译：迄今为止，如何在整个生命周期内优化消费和投资组合选择的问题已在文献中广泛讨论。在本文中，我们重点介绍退休人员在其剩余生命中的最佳消费和投资组合选择。我们应用死亡率的逻辑模型，从而对根据经验观察到的退休期间死亡率的增加进行建模。通过将Hamilton-Jacobi-Bellmann方程简化为包含死亡率的普通微分函数（ODF）的显式解，可以建立最佳的消费策略和投资组合选择。一个普遍的发现是，对于恒定死亡率，对于恒定死亡率，选择固定资产组合的默顿-萨缪尔森结果得到了证实。投资组合的选择仅受资产的风险和收益以及退休人员的风险规避的影响。为了在现实情况下获得特定的最佳消费策略，将死亡率的逻辑模型应用于德意志联邦共和国2006/2008年统计年鉴的数据。通过数值方法获得ODF的最佳初始值。该解决方案使最佳消费与财富的比率大大提高，直至约92年，然后急剧下降。遗赠动机可以抑制消费比率的起伏幅度，但不会改变基本形状。

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