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arXiv 1803.04591q-fin.STq-fin.CP
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基于反馈控制的股票交易鲁棒正期望定理的推广

A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control

Atul Deshpande, B. Ross Barmish

摘要:

本文的出发点是所谓的鲁棒正期望(RPE)定理,这一结果出现在文献中的上下文中的同时多空股票交易。该定理指出,使用两个专门构造的线性反馈交易控制器的组合,一个长,一个短,所得到的收益-损失函数的期望值保证是鲁棒的积极相对于一个大类的随机过程的股票价格。本文的主要结果是这个定理的推广。而以前的工作适用于一个单一的股票,在本文中,我们考虑一对股票。为此,我们对它们的预期收益率做了两个假设。第一个假设涉及两个股票之间的价格相关性,第二个假设涉及一个有界的非零动量条件。与已知的不确定性界与这些假设相关的参数,我们的新版本的RPE定理提供了必要和充分条件下的控制器的正反馈参数K鲁棒正期望是有保证的。我们还证明,我们的结果推广了现有的单股票的情况下。最后,值得注意的是,我们的研究结果也可以在配对交易的背景下进行解释。

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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