适用于所有时间范围的最优投资和马丁边界

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英文标题：
《Optimal investment for all time horizons and Martin boundary of
  space-time diffusions》
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作者：
Sergey Nadtochiy and Michael Tehranchi
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最新提交年份：
2014
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英文摘要：
  This paper is concerned with the axiomatic foundation and explicit construction of a general class of optimality criteria that can be used for investment problems with multiple time horizons, or when the time horizon is not known in advance. Both the investment criterion and the optimal strategy are characterized by the Hamilton-Jacobi-Bellman equation on a semi-infinite time interval. In the case when this equation can be linearized, the problem reduces to a time-reversed parabolic equation, which cannot be analyzed via the standard methods of partial differential equations. Under the additional uniform ellipticity condition, we make use of the available description of all minimal solutions to such equations, along with some basic facts from potential theory and convex analysis, to obtain an explicit integral representation of all positive solutions. These results allow us to construct a large family of the aforementioned optimality criteria, including some closed form examples in relevant financial models.
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中文摘要：
本文研究了一类可用于具有多个时间范围或时间范围未知的投资问题的最优性准则的公理化基础和显式构造。投资准则和最优策略均由半无限时间区间上的Hamilton-Jacobi-Bellman方程描述。在这个方程可以线性化的情况下，问题会简化为一个时间反转抛物方程，无法通过偏微分方程的标准方法进行分析。在附加一致椭圆条件下，我们利用这类方程所有极小解的现有描述，以及势理论和凸分析中的一些基本事实，得到了所有正解的显式积分表示。这些结果使我们能够构建上述最优性标准的大家族，包括相关金融模型中的一些封闭形式示例。
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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：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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关键词：Differential Applications Construction Optimization Presentation