英文标题：
《Optimally Investing to Reach a Bequest Goal》
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作者：
Erhan Bayraktar and Virginia R. Young
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最新提交年份：
2016
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英文摘要：
We determine the optimal strategy for investing in a Black-Scholes market in order to maximize the probability that wealth at death meets a bequest goal $b$, a type of goal-seeking problem, as pioneered by Dubins and Savage (1965, 1976). The individual consumes at a constant rate $c$, so the level of wealth required for risklessly meeting consumption equals $c/r$, in which $r$ is the rate of return of the riskless asset. Our problem is related to, but different from, the goal-reaching problems of Browne (1997). First, Browne (1997, Section 3.1) maximizes the probability that wealth reaches $b < c/r$ before it reaches $a < b$. Browne\'s game ends when wealth reaches $b$. By contrast, for the problem we consider, the game continues until the individual dies or until wealth reaches 0; reaching $b$ and then falling below it before death does not count. Second, Browne (1997, Section 4.2) maximizes the expected discounted reward of reaching $b > c/r$ before wealth reaches $c/r$. If one interprets his discount rate as a hazard rate, then our two problems are {\\it mathematically} equivalent for the special case for which $b > c/r$, with ruin level $c/r$. However, we obtain different results because we set the ruin level at 0, thereby allowing the game to continue when wealth falls below $c/r$.
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中文摘要：
我们确定投资布莱克-斯科尔斯市场的最佳策略，以最大限度地提高死亡财富达到遗产目标b$的概率，这是一种目标寻求问题，由杜宾斯和萨维奇（Dubins and Savage，19651976）率先提出。个人以固定利率消费$c$，因此无风险满足消费所需的财富水平等于$c/r$，其中$r$是无风险资产的回报率。我们的问题与Browne（1997）的目标达成问题有关，但不同。首先，Browne（1997年，第3.1节）最大化了财富在达到$a<b$之前达到$b<c/r$的概率。当财富达到亿美元时，布朗的游戏就结束了。相比之下，对于我们考虑的问题，游戏一直持续到个人死亡或财富达到0；达到b美元，然后在死前跌破它并不算在内。其次，Browne（1997年，第4.2节）在财富达到$c/r$之前，将预期的折扣回报最大化，即达到$b>c/r$。如果一个人把他的贴现率解释为一个风险率，那么我们的两个问题对于特殊情况是{\\it数学上}等价的，对于这种特殊情况，$b>c/r$，破产水平为$c/r$。然而，我们得到了不同的结果，因为我们将破产水平设置为0，从而允许当财富低于$c/r$时博弈继续。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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