英文标题：
《Scenario generation for single-period portfolio selection problems with
  tail risk measures: coping with high dimensions and integer variables》
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作者：
Jamie Fairbrother, Amanda Turner, Stein Wallace
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最新提交年份：
2017
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英文摘要：
  In this paper we propose a problem-driven scenario generation approach to the single-period portfolio selection problem which use tail risk measures such as conditional value-at-risk. Tail risk measures are useful for quantifying potential losses in worst cases. However, for scenario-based problems these are problematic: because the value of a tail risk measure only depends on a small subset of the support of the distribution of asset returns, traditional scenario based methods, which spread scenarios evenly across the whole support of the distribution, yield very unstable solutions unless we use a very large number of scenarios. The proposed approach works by prioritizing the construction of scenarios in the areas of a probability distribution which correspond to the tail losses of feasible portfolios.   The proposed approach can be applied to difficult instances of the portfolio selection problem characterized by high-dimensions, non-elliptical distributions of asset returns, and the presence of integer variables. It is also observed that the methodology works better as the feasible set of portfolios becomes more constrained. Based on this fact, a heuristic algorithm based on the sample average approximation method is proposed. This algorithm works by adding artificial constraints to the problem which are gradually tightened, allowing one to telescope onto high quality solutions.
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中文摘要：
在本文中，我们提出了一种问题驱动的情景生成方法来解决单期投资组合选择问题，该方法使用尾部风险度量，如条件风险价值。尾部风险度量有助于量化最坏情况下的潜在损失。然而，对于基于情景的问题，这些都是有问题的：因为尾部风险度量的价值只取决于资产回报分布支持的一小部分，传统的基于情景的方法（将情景均匀地分布在整个分布支持上）会产生非常不稳定的解决方案，除非我们使用非常多的情景。所提出的方法通过在概率分布区域中优先构建场景来工作，该概率分布对应于可行投资组合的尾部损失。该方法适用于高维、非椭圆分布的资产收益率和存在整数变量的投资组合选择问题。还观察到，当可行的投资组合集变得更加受限时，该方法的效果更好。基于这一事实，提出了一种基于样本平均近似法的启发式算法。该算法的工作原理是向问题添加人工约束，这些约束会逐渐收紧，从而使人们能够看到高质量的解决方案。
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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：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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