英文标题：
《On Inefficiency of Markowitz-Style Investment Strategies When Drawdown
  is Important》
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作者：
Chung-Han Hsieh and B. Ross Barmish
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最新提交年份：
2018
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英文摘要：
  The focal point of this paper is the issue of \"drawdown\" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to subsequent lows. Motivated by the fact that this issue is of paramount concern to conservative investors, we dispense with the classical variance as the risk metric and work with drawdown and mean return as the risk-reward pair. In this setting, the main results in this paper address the so-called \"efficiency\" of linear time-invariant (LTI) investment feedback strategies which correspond to Markowitz-style schemes in the finance literature. Our analysis begins with the following principle which is widely used in finance: Given two investment opportunities, if one of them has higher risk and lower return, it will be deemed to be inefficient or strictly dominated and generally rejected in the marketplace. In this framework, with risk-reward pair as described above, our main result is that classical Markowitz-style strategies are inefficient. To establish this, we use a new investment strategy which involves a time-varying linear feedback block K(k), called the drawdown modulator. Using this instead of the original LTI feedback block K in the Markowitz scheme, the desired domination is obtained. As a bonus, it is also seen that the modulator assures a worst-case level of drawdown protection with probability one.
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中文摘要：
本文的重点是在股票市场的递归下注场景和相关应用中出现的“提款”问题。粗略地说，资金减少被理解为财富随时间从峰值下降到随后的低点。出于保守投资者最为关注这一问题的动机，我们放弃了经典方差作为风险度量，将提取和平均回报作为风险-回报对。在这种背景下，本文的主要结果解决了线性时不变（LTI）投资反馈策略的所谓“效率”，这与金融文献中的马科维茨式方案相对应。我们的分析从以下在金融领域广泛使用的原则开始：给定两个投资机会，如果其中一个具有较高的风险和较低的回报，则将被视为效率低下或被严格控制，并在市场上普遍被拒绝。在这个框架中，使用如上所述的风险-回报对，我们的主要结果是经典的马科维茨式策略是低效的。为了实现这一点，我们使用了一种新的投资策略，该策略涉及一个时变线性反馈块K（K），称为下降调制器。使用该方法代替Markowitz格式中的原始LTI反馈块K，可以获得所需的控制。此外，还可以看到，调制器以概率1确保了最坏情况下的水位下降保护水平。
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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：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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