摘要翻译：
我们揭示了两个问题之间的一个有趣的凸对偶关系：(a)当消费率是随机的，当个人可以在Black-Scholes金融市场上投资时，最小化终身破产概率；(b)控制器与塞子问题，其中控制器控制一个过程的漂移和波动，以使基于该过程的运行奖励最大化，塞子选择停止运行奖励的时间，并在该时间向控制器奖励最终数量。我们的主要目的是证明最小破产概率是其Hamilton-Jacobi-Bellman方程的唯一经典解，它的随机表示不像效用最大化问题那样具有经典形式（即目标对状态变量初值的依赖是隐式的），这是一个非线性边值问题。我们通过利用(a)和(b)之间的凸对偶关系来建立我们的目标。
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英文标题：
《Proving Regularity of the Minimal Probability of Ruin via a Game of
  Stopping and Control》
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作者：
Erhan Bayraktar, Virginia R. Young
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最新提交年份：
2009
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分类信息：

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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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：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 reveal an interesting convex duality relationship between two problems: (a) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market; (b) a controller-and-stopper problem, in which the controller controls the drift and volatility of a process in order to maximize a running reward based on that process, and the stopper chooses the time to stop the running reward and rewards the controller a final amount at that time. Our primary goal is to show that the minimal probability of ruin, whose stochastic representation does not have a classical form as does the utility maximization problem (i.e., the objective's dependence on the initial values of the state variables is implicit), is the unique classical solution of its Hamilton-Jacobi-Bellman (HJB) equation, which is a non-linear boundary-value problem. We establish our goal by exploiting the convex duality relationship between (a) and (b).
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PDF链接：
https://arxiv.org/pdf/0704.2244