The present paper combines nonlinear shrinkage with the multivariate generalized hyperbolic (MGHyp) distribution, thereby extending a flexible parametric model to high dimensions. An expectation–maximization (EM) algorithm is developed that is fast, stable, and applicable in high dimensions. Theoretical arguments for the monotonicity of the proposed algorithm are provided and it is shown in simulations that it is able to accurately retrieve parameter estimates. Finally, in an extensive Markowitz portfolio optimization analysis, the approach is compared to state-of-the-art benchmark models. The proposed model excels with a strong out-of-sample portfolio performance combined with a comparably low turnover.

中文翻译：

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将 MGHyp 分布与非线性收缩相结合来建模金融资产回报

本文将非线性收缩与多元广义双曲（MGHyp）分布相结合，从而将灵活的参数模型扩展到高维度。开发了一种快速、稳定且适用于高维的期望最大化 (EM) 算法。提供了所提出算法的单调性的理论论证，并且仿真表明它能够准确地检索参数估计。最后，在广泛的马科维茨投资组合优化分析中，将该方法与最先进的基准模型进行了比较。所提出的模型具有出色的样本外投资组合表现以及相对较低的换手率。