ASSET ALLOCATION AND ANNUITY‐PURCHASE STRATEGIES TO MINIMIZE THE PROBABILITY OF FINANCIAL RUIN
ASSET ALLOCATION AND ANNUITY‐PURCHASE STRATEGIES TO MINIMIZE THE PROBABILITY OF FINANCIAL RUIN
复制标题
DOI：
10.1111/j.1467-9965.2006.00288.x
复制
发表时间：
2006-08
影响因子：
1.6
通讯作者：
M. Milevsky;K. Moore;V. Young
中科院分区：
文献类型：
--
作者：
M. Milevsky;K. Moore;V. Young
本文给出了以终生破产概率最小为目标的退休人员的最优投资和年化策略，即在个人还活着的时候，固定消费策略导致零财富的概率。保险经济学文献中最近的论文研究了效用最大化的年化策略。概率、金融和风险管理文献中的其他人已经得出了缺口最小化投资和对冲策略，在初始资本有限的情况下。这篇论文将这两个研究线索结合在一起。我们的模型假设退休人员目前没有足够的财富购买终身年金，这将产生她外在期望的固定消费水平。她寻求资产配置和年化策略，将终身破产的可能性降至最低。我们证明，由于投资者目标的二元性，她不会年化她的任何财富，直到她能够用终身年金完全覆盖她想要的消费。我们导出了一个控制破产概率和最优策略的变分不等式，并证明了该问题可以转化为一个相关的最优停止问题，从而产生一个更容易处理的自由边界问题。我们用数值方法计算了破产概率和最优策略，并考察了当我们改变死亡率假设和金融模型参数时，它们是如何变化的。此外，对于指数未来寿命的特殊情况，我们显式地解决了(对偶)问题。作为我们计算的副产品，我们能够量化由于能够动态管理投资组合和购买年金而导致的终身破产概率的降低。
In this paper, we derive the optimal investment and annuitization strategies for a retiree whose objective is to minimize the probability of lifetime ruin, namely the probability that a fixed consumption strategy will lead to zero wealth while the individual is still alive. Recent papers in the insurance economics literature have examined utility‐maximizing annuitization strategies. Others in the probability, finance, and risk management literature have derived shortfall‐minimizing investment and hedging strategies given a limited amount of initial capital. This paper brings the two strands of research together. Our model pre‐supposes a retiree who does not currently have sufficient wealth to purchase a life annuity that will yield her exogenously desired fixed consumption level. She seeks the asset allocation and annuitization strategy that will minimize the probability of lifetime ruin. We demonstrate that because of the binary nature of the investor's goal, she will not annuitize any of her wealth until she can fully cover her desired consumption with a life annuity. We derive a variational inequality that governs the ruin probability and the optimal strategies, and we demonstrate that the problem can be recast as a related optimal stopping problem which yields a free‐boundary problem that is more tractable. We numerically calculate the ruin probability and optimal strategies and examine how they change as we vary the mortality assumption and parameters of the financial model. Moreover, for the special case of exponential future lifetime, we solve the (dual) problem explicitly. As a byproduct of our calculations, we are able to quantify the reduction in lifetime ruin probability that comes from being able to manage the investment portfolio dynamically and purchase annuities.