基于均方混合模型的随机支配与均方-风险最优投资组合问题讨论
Efficient frontiers for portfolios under SSD and law-invariant risk measures with hyperbolic return distributions
AI总结：
本文基于均方混合模型，探讨了在一般均风险模型下如何通过调整收益率向量获得均风险前沿投资组合的闭式解，提出了随机支配关系的充分条件。
摘要：
经典的马科维茨均方模型使用方差作为风险度量，并通过标准优化技术以闭式形式计算前沿投资组合。对于此类封闭形式最优投资组合，一般均风险模型难以获得。在本笔记中，假设收益率遵循正常均方混合（NMVM）分布的类别，我们获得在均风险标准下，当风险由一般类别的法不变凸风险度量建模时，前沿投资组合的闭式表达式。为实现此目标，我们首先提出NMVM模型上随机支配关系的充分条件，并将此结果应用于推导前沿投资组合的闭式解。本文的主要结果表明，当收益率向量遵循NMVM分布类别时，相关的均风险前沿投资组合可通过优化一个适当调整的马科维茨均方模型来获得。
英文摘要：
In the classical Markowitz mean variance framework, risk is measured by variance, and the portfolios on the efficient frontier can be derived in closed form using standard optimization methods. For broader mean risk formulations, however, obtaining closed form optimal portfolios is typically difficult. In this work, we derive explicit expressions for frontier portfolios corresponding to arbitrary law-invariant convex risk measures, assuming that the return vector follows a normal mean variance mixture distribution. Our approach first establishes stochastic dominance relations within the family of normal mean variance mixture models, and then leverages these relations to derive closed-form representations of frontier portfolios. The central finding demonstrates that when asset returns are described by a normal mean variance mixture models the associated mean risk efficient frontier can be obtained by solving a Markowitz mean variance problem for a suitably transformed return vector. The paper also extends the CAPM framework to the context of a normal mean variance mixture distribution.
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