英文标题：
《On portfolios generated by optimal transport》
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作者：
Ting-Kam Leonard Wong
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最新提交年份：
2017
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英文摘要：
First introduced by Fernholz in stochastic portfolio theory, functionally generated portfolio allows its investment performance to be attributed to directly observable and easily interpretable market quantities. In previous works we showed that Fernholz\'s multiplicatively generated portfolio has deep connections with optimal transport and the information geometry of exponentially concave functions. Recently, Karatzas and Ruf introduced a new additive portfolio generation whose relation with optimal transport was studied by Vervuurt. We show that additively generated portfolio can be interpreted in terms of the well-known dually flat information geometry of Bregman divergence. Moreover, we characterize, in a sense to be made precise, all possible forms of functional portfolio constructions that contain additive and multiplicative generations as special cases. Each construction involves a divergence functional on the unit simplex measuring the market volatility captured, and admits a pathwise decomposition for the portfolio value. We illustrate with an empirical example.
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中文摘要：
由Fernholz在随机投资组合理论中首次引入的功能生成投资组合允许其投资绩效归因于直接可观察且易于解释的市场数量。在以前的工作中，我们证明了Fernholz的乘法生成投资组合与最优传输和指数凹函数的信息几何有着深刻的联系。最近，Karatzas和Ruf引入了一个新的加性组合世代，Vervuurt研究了其与最优运输的关系。我们证明，加性生成的投资组合可以用著名的布雷格曼散度的对偶平坦信息几何来解释。此外，在某种意义上，我们将包含加法和乘法代的所有可能形式的函数组合结构作为特例进行了刻画。每种构造都涉及一个度量所捕获市场波动率的单位单纯形上的分歧函数，并允许对投资组合价值进行路径分解。我们用一个实证例子加以说明。
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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：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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