论文标题
基于平均变化混合模型的随机优势和均值最佳投资组合问题的讨论
A discussion of stochastic dominance and mean-risk optimal portfolio problems based on mean-variance-mixture models
论文作者
论文摘要
经典的Markowitz均值变化模型将方差用作风险度量，并使用标准优化技术以封闭形式计算边境投资组合。对于一般的平均风险模型，这种封闭形式的最佳投资组合很难获得。在本说明中，假设收益遵循正常的均值变化混合物（NMVM）分布的类别，则在均值危险凸风险衡量标准的风险时，我们在均值风险标准下获得边境投资组合的封闭形式表达式。为了实现这一目标，我们首先为NMVM模型的随机优势关系提供了足够的条件，我们将此结果应用于为边境投资组合提供封闭形式的解决方案。 本文我们的主要结果指出，当返回向量遵循NMVM分布的类别时，可以通过优化具有适当调整的返回向量的Markowitz均值变化模型来获得相关的平均风险前沿投资组合。
The classical Markowitz mean-variance model uses variance as a risk measure and calculates frontier portfolios in closed form by using standard optimization techniques. For general mean-risk models such closed form optimal portfolios are difficult to obtain. In this note, assuming returns follow the class of normal mean-variance mixture (NMVM) distributions, we obtain closed form expressions for frontier portfolios under mean-risk criteria when risk is modeled by the general class of law invariant convex risk measures. To achieve this goal, we first present a sufficient condition for the stochastic dominance relation on NMVM models and we apply this result to derive closed form solution for frontier portfolios. Our main result in this paper states that when return vectors follow the class of NMVM distributions the associated mean-risk frontier portfolios can be obtained by optimizing a Markowitz mean-variance model with an appropriately adjusted return vector.
