摘要翻译：
我们在经典的Markowitz均值-方差框架下考虑投资组合选择问题，并将其转化为一个约束最小二乘回归问题。我们建议在目标函数中加入一个与投资组合权重绝对值之和成正比的惩罚。这种惩罚规则化（稳定）优化问题，鼓励稀疏投资组合（即只有少量活跃头寸的投资组合），并允许考虑交易成本。作为特殊情况，我们的方法恢复了无空头仓位的投资组合，但允许有限数量的空头仓位。我们在Fama和French构建的两个基准数据集上实现了该方法。仅使用少量的训练数据，我们构造出的投资组合，其样本外的表现，如夏普比率所衡量的，一致地和显著地优于朴素的均匀加权投资组合，如最近的文献所示，均匀加权投资组合构成了一个非常困难的基准。
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英文标题：
《Sparse and stable Markowitz portfolios》
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作者：
Joshua Brodie, Ingrid Daubechies, Christine De Mol, Domenico Giannone,
  Ignace Loris
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最新提交年份：
2008
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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：Mathematics        数学
二级分类：Functional Analysis        功能分析
分类描述：Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
Banach空间，函数空间，实函数，积分变换，分布理论，测度理论
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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
  We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights. This penalty regularizes (stabilizes) the optimization problem, encourages sparse portfolios (i.e. portfolios with only few active positions), and allows to account for transaction costs. Our approach recovers as special cases the no-short-positions portfolios, but does allow for short positions in limited number. We implement this methodology on two benchmark data sets constructed by Fama and French. Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the naive evenly-weighted portfolio which constitutes, as shown in recent literature, a very tough benchmark.
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PDF链接：
https://arxiv.org/pdf/0708.0046