摘要翻译：
我们发现了一个投资者在一个具有风险和无风险资产的市场上投资，并且可以购买可逆的终身年金的最小终身破产概率。终身年金的退保费用是其价值的一个比例。当风险资产和无风险资产的价值与终身年金的退保价值之和达到零时，即为破产。在两种情况下，我们找到了最优的投资策略和最优的年金购买和退保策略：（一）允许风险资产和无风险资产的价值为负值，终身年金的估算退保价值保持为正；或者(ii)风险资产和无风险资产的价值要求为非负值。在第一种情况下，尽管个人有随时买卖的灵活性，但我们发现，个人不会购买终身年金，除非她能够通过年金支付所有的消费，而且她永远不会出售自己的年金。在第二种情况下，个人交出的年金收入刚好足以保持她的总资产为正。然而，在第二种情况下，个人的年金购买策略取决于比例退保费用的大小。当费用足够大时，个人不会购买终身年金，除非她能覆盖她的所有消费，即所谓的安全水平。当收费足够小时，个人将以低于这一安全水平的财富购买终身年金。
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英文标题：
《Optimal Reversible Annuities to Minimize the Probability of Lifetime
  Ruin》
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作者：
Ting Wang, Virginia R. Young
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
  We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a reversible life annuity. The surrender charge of a life annuity is a proportion of its value. Ruin occurs when the total of the value of the risky and riskless assets and the surrender value of the life annuity reaches zero. We find the optimal investment strategy and optimal annuity purchase and surrender strategies in two situations: (i) the value of the risky and riskless assets is allowed to be negative, with the imputed surrender value of the life annuity keeping the total positive; or (ii) the value of the risky and riskless assets is required to be non-negative. In the first case, although the individual has the flexiblity to buy or sell at any time, we find that the individual will not buy a life annuity unless she can cover all her consumption via the annuity and she will never sell her annuity. In the second case, the individual surrenders just enough annuity income to keep her total assets positive. However, in this second case, the individual's annuity purchasing strategy depends on the size of the proportional surrender charge. When the charge is large enough, the individual will not buy a life annuity unless she can cover all her consumption, the so-called safe level. When the charge is small enough, the individual will buy a life annuity at a wealth lower than this safe level.
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PDF链接：
https://arxiv.org/pdf/1001.4270