Scenario generation for portfolio selection problems with tail risk measure
Scenario generation for portfolio selection problems with tail risk measure
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发表时间：
2015-11
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通讯作者：
Jamie Fairbrother;Amanda G. Turner;S. Wallace
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作者：
Jamie Fairbrother;Amanda G. Turner;S. Wallace
尾部风险度量，如条件风险价值，在投资组合选择的背景下，对于量化最坏情况下的潜在损失是有用的。然而，对于基于贝叶斯的问题，这些是有问题的：因为尾部风险度量的值只取决于资产收益分布的支持的一个小子集，传统的基于场景的方法，将场景均匀地分布在整个分布的支持上，产生非常不稳定的解决方案，除非我们使用非常大的场景。在本文中，我们提出了一个问题驱动的情景生成方法的投资组合选择问题，使用尾部风险度量的资产收益率有椭圆或近椭圆分布。实际上，我们的方法优先考虑在分布区域中构建场景，这些场景对应于可行投资组合的尾部损失。当资产收益率的分布是正相关的和重尾的时，该方法特别有效，并且当我们收紧对可行资产的约束时，表现会有所改善。
Tail risk measures such as the conditional value-at-risk are useful in the context of portfolio selection 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 scenarios. In this paper we propose a problem-driven scenario generation methodology for portfolio selection problems using a tail risk measure where the the asset returns have elliptical or near-elliptical distribution. Our approach in effect prioritizes the construction of scenarios in the areas of the distribution which correspond to the tail losses of feasible portfolios. The methodology is shown to work particularly well when the distribution of assets returns are positively correlated and heavy-tailed, and the performance is shown to improve as we tighten the constraints on feasible assets.