英文标题：
《A Generalization of the Robust Positive Expectation Theorem for Stock
Trading via Feedback Control》
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作者：
Atul Deshpande and B. Ross Barmish
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最新提交年份：
2018
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英文摘要：
The starting point of this paper is the so-called Robust Positive Expectation (RPE) Theorem, a result which appears in literature in the context of Simultaneous Long-Short stock trading. This theorem states that using a combination of two specially-constructed linear feedback trading controllers, one long and one short, the expected value of the resulting gain-loss function is guaranteed to be robustly positive with respect to a large class of stochastic processes for the stock price. The main result of this paper is a generalization of this theorem. Whereas previous work applies to a single stock, in this paper, we consider a pair of stocks. To this end, we make two assumptions on their expected returns. The first assumption involves price correlation between the two stocks and the second involves a bounded non-zero momentum condition. With known uncertainty bounds on the parameters associated with these assumptions, our new version of the RPE Theorem provides necessary and sufficient conditions on the positive feedback parameter K of the controller under which robust positive expectation is assured. We also demonstrate that our result generalizes the one existing for the single-stock case. Finally, it is noted that our results also can be interpreted in the context of pairs trading.
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中文摘要：
本文的出发点是所谓的稳健正期望（RPE）定理，这是一个出现在文献中的同时进行多空股票交易的结果。该定理表明，使用两个特殊构造的线性反馈交易控制器（一个长控制器和一个短控制器）的组合，所得到的损益函数的期望值对于一大类股票价格随机过程是鲁棒正的。本文的主要结果是对该定理的推广。鉴于之前的工作适用于单个股票，在本文中，我们考虑一对股票。为此，我们对他们的预期回报做出了两个假设。第一个假设涉及两支股票之间的价格相关性，第二个假设涉及有界非零动量条件。在已知与这些假设相关的参数的不确定性界的情况下，我们新版本的RPE定理提供了控制器正反馈参数K的充要条件，在此条件下，鲁棒正期望得到保证。我们还证明了我们的结果推广了单股票情况下的结果。最后，值得注意的是，我们的结果也可以在配对交易的背景下进行解释。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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