摘要翻译：
大投资组合的优化对估计误差表现出内在的不稳定性。这就提出了一个根本问题，因为在样本波动下不稳定的解决方案对于给定的样本来说可能看起来是最优的，但实际上就平均风险而言远远不是最优的。本文从统计学习理论的角度对该问题进行了探讨。不稳定的发生与过拟合密切相关，而过拟合可以用已知的正则化方法来避免。我们展示了以预期缺口作为风险度量的正则化投资组合优化是如何与支持向量回归相关联的。预算限制要求进行修改。我们给出了最终的优化问题并讨论了解决方案。权重向量的L2范数作为正则化子，对应一个多样化“压力”。这意味着多样化除了通过其他资产的向上波动来抵消某些资产的向下波动之外，也是至关重要的，因为它提高了解决方案的稳定性。我们在这里提供的方法允许在一个框架中同时处理优化和多样化，使投资者能够根据可用数据集的大小在两者之间进行权衡。
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英文标题：
《Regularizing Portfolio Optimization》
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作者：
Susanne Still and Imre Kondor
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最新提交年份：
2009
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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：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
  The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification "pressure". This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade-off between the two, depending on the size of the available data set.
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PDF链接：
https://arxiv.org/pdf/0911.1694