Ruined Moments in Your Life: How Good are the Approximations?
Ruined Moments in Your Life: How Good are the Approximations?
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你生命中被毁掉的时刻：近似值有多好？
DOI：
10.2139/ssrn.495703
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
M. Milevsky
中科院分区：
文献类型：
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作者：
Jin Wang;Huang Huaxiong;M. Milevsky
本文应用数值PDE求解技术计算了终身破产概率，即在随机投资收益和寿命分布下，固定退休消费策略导致财务破产的概率。利用从美国金融数据中获得的股票市场参数，我们得出结论，一个65岁的退休人员需要30倍于他们期望的年（实际）消费，才能产生95%的可持续性可能性，这相当于5%的终身破产概率，如果资金投资于一个多元化的股票投资组合。30比1的安全边际可以与与通胀挂钩的收入的相关年金系数形成对比，后者将产生零终身破产的可能性。然后，我们的论文将数值PDE值与文献中提出的各种矩匹配和其他近似值进行比较，以计算破产的终生概率。我们的研究结果表明，只要基础投资回报的波动率不超过每年的四分之三= 30%，这与资本市场的历史是一致的，那么倒数伽马近似就提供了准确的拟合。在较高的波动水平下，矩匹配近似失效，我们为这种现象提供了一些理论原因。我们的数值和方法结果应该对学者和实践者感兴趣，他们对近似随机现值的方法感兴趣，以及对人类生命周期结束时可持续消费和提取率的计算方法感兴趣。
In this paper we implement numerical PDE solution techniques to compute the probability of lifetime ruin which is the probability that a fixed retirement consumption strategy will lead to financial insolvency under stochastic investment returns and lifetime distribution. Using equity market parameters derived from US-based financial data we conclude that a 65-year-old retiree requires 30 times their desired annual (real) consumption to generate a 95% probability of sustainability, which is equivalent to a 5% probability of lifetime ruin, if the funds are invested in a well-diversified equity portfolio. The 30-to-1 margin of safety can be contrasted with the relevant annuity factor for an inflation-linked income which would generate a zero probability of lifetime ruin. Our paper then goes on to compare the numerical PDE values with various moment matching and other approximations that have been proposed in the literature to compute the lifetime probability of ruin. Our results indicate that the Reciprocal Gamma approximation provides an accurate fit as long as the volatility of the underlying investment return does not exceed three-fourths = 30% per annum, which is consistent with capital market history. At higher levels of volatility the moment matching approximations break down and we provide some theoretical reasons for this phenomena. Our numerical and methodological results should be of interest to both academics and practitioners who are interested in methods of approximating stochastic present values as well as methods for computing sustainable consumption and withdrawal rates towards the end of the human life cycle.