摘要翻译：
经典的均值-方差投资组合理论告诉我们如何构造一个在给定的收益波动水平下具有最大期望收益的资产组合。效用理论允许投资者沿着这个有效边界选择一个点，这个点可以最优地平衡她对超额预期收益的渴望和她不愿承担风险的意愿。假定未来资产收益分布的均值和协方差是已知的，因此不确定性的唯一来源是价格演化的随机部分。在现实世界中，我们还有另一个不确定性来源--我们估计但不确定未来资产收益的均值和协方差。本文解释了如何构造未来收益具有不确定均值和协方差的资产的均值-方差最优投资组合。结果形式简单、直观，并且可以很容易地合并到优化器中。
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英文标题：
《Portfolio Optimization Under Uncertainty》
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作者：
Alex Dannenberg (Pine Mountain Capital Management)
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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：
  Classical mean-variance portfolio theory tells us how to construct a portfolio of assets which has the greatest expected return for a given level of return volatility. Utility theory then allows an investor to choose the point along this efficient frontier which optimally balances her desire for excess expected return against her reluctance to bear risk. The means and covariances of the distributions of future asset returns are assumed to be known, so the only source of uncertainty is the stochastic piece of the price evolution.   In the real world, we have another source of uncertainty - we estimate but don't know with certainty the means and covariances of future asset returns. This note explains how to construct mean-variance optimal portfolios of assets whose future returns have uncertain means and covariances. The result is simple in form, intuitive, and can easily be incorporated in an optimizer.
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PDF链接：
https://arxiv.org/pdf/0908.1444