英文标题：
《Portfolio Optimization under Expected Shortfall: Contour Maps of
  Estimation Error》
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作者：
Fabio Caccioli, Imre Kondor, G\\\'abor Papp
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最新提交年份：
2015
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英文摘要：
  The contour maps of the error of historical resp. parametric estimates for large random portfolios optimized under the risk measure Expected Shortfall (ES) are constructed. Similar maps for the sensitivity of the portfolio weights to small changes in the returns as well as the VaR of the ES-optimized portfolio are also presented, along with results for the distribution of portfolio weights over the random samples and for the out-of-sample and in-the-sample estimates for ES. The contour maps allow one to quantitatively determine the sample size (the length of the time series) required by the optimization for a given number of different assets in the portfolio, at a given confidence level and a given level of relative estimation error. The necessary sample sizes invariably turn out to be unrealistically large for any reasonable choice of the number of assets and the confidence level. These results are obtained via analytical calculations based on methods borrowed from the statistical physics of random systems, supported by numerical simulations.
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中文摘要：
历史响应误差等值线图。构造了在风险度量期望短缺（ES）下优化的大型随机投资组合的参数估计。此外，还提供了投资组合权重对ES优化投资组合的收益率和VaR微小变化的敏感性的类似映射图，以及ES的随机样本和样本外和样本内估计的投资组合权重分布结果。等高线图允许在给定置信水平和给定相对估计误差水平下，定量确定组合中给定数量不同资产的优化所需的样本量（时间序列的长度）。对于资产数量和置信水平的任何合理选择而言，必要的样本量总是不切实际的大。这些结果是通过基于借鉴随机系统统计物理方法的分析计算获得的，并得到了数值模拟的支持。
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分类信息：

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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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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