英文标题：
《On the solution uniqueness in portfolio optimization and risk analysis》
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作者：
Bogdan Grechuk and Andrzej Palczewski and Jan Palczewski
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最新提交年份：
2020
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英文摘要：
We consider the issue of solution uniqueness for portfolio optimization problem and its inverse for asset returns with a finite number of possible scenarios. The risk is assessed by deviation measures introduced by [Rockafellar et al., Mathematical Programming, Ser. B, 108 (2006), pp. 515-540] instead of variance as in the Markowitz optimization problem. We prove that in general one can expect uniqueness neither in forward nor in inverse problems. We discuss consequences of that non-uniqueness for several problems in risk analysis and portfolio optimization, including capital allocation, risk sharing, cooperative investment, and the Black-Litterman methodology. In all cases, the issue with non-uniqueness is closely related to the fact that subgradient of a convex function is non-unique at the points of non-differentiability. We suggest methodology to resolve this issue by identifying a unique \"special\" subgradient satisfying some natural axioms. This \"special\" subgradient happens to be the Stainer point of the subdifferential set.
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中文摘要：
我们考虑了在有限个可能情景下，资产组合优化问题的解唯一性及其逆问题。风险是通过【Rockafellar等人，《数学规划》，Ser.B，108（2006），第515-540页】引入的偏差度量来评估的，而不是马科维茨优化问题中引入的方差。我们证明了在一般情况下，无论是正问题还是反问题，都不能期望唯一性。我们讨论了这种非唯一性对风险分析和投资组合优化中几个问题的影响，包括资本分配、风险分担、合作投资和Black Litterman方法。在所有情况下，非唯一性问题都与凸函数的次梯度在不可微点处非唯一这一事实密切相关。我们建议通过确定满足某些自然公理的唯一“特殊”次梯度来解决这个问题。这个“特殊”次梯度恰好是次微分集的Stainer点。
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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：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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