论文标题
基于资产动力学的神经网络敏感性的投资组合优化尊重常见驱动因素
Portfolio Optimization based on Neural Networks Sensitivities from Assets Dynamics respect Common Drivers
论文作者
论文摘要
我们提出了一个建模资产和投资组合动力学的框架，将这些信息纳入了投资组合优化。对于此框架，我们介绍了共同点原则，为最佳选择投资组合驱动程序作为通用驱动程序提供了解决方案。投资组合组成的动力学由部分微分方程建模，并与神经网络近似。相对于共同驱动器的敏感性是通过自动伴随分化获得的。有关资产动力学的信息通过灵敏度纳入投资组合优化。投资组合成分相对于其共同驱动因素嵌入了敏感性的空间中，并且该空间中的距离矩阵（称为灵敏度矩阵）用于求解凸的优化以进行多样化。灵敏度矩阵测量了由共同驱动程序的回报形成的向量空间上投资组合成分的投影的相似性，并用于优化在特质和系统性风险上的多元化，同时通过返回动态增加方向性和未来行为信息。对于投资组合优化，我们在灵敏度矩阵上执行层次聚类。据作者所知，这是第一次将敏感性与神经网络近似的动力学用于投资组合优化。其次，使用灵敏度矩阵上的层次聚类用于解决凸优化问题，并结合了这些灵敏度的层次信息。第三，公共和列出的变量可用于通过敏感性空间相对于最佳投资组合驱动程序来获得最大的特质和系统的多样化。在许多其他针对不同市场和实际数据集的样本外方法方面，我们在许多实验中达到了表现。
We present a framework for modeling asset and portfolio dynamics, incorporating this information into portfolio optimization. For this framework, we introduce the Commonality Principle, providing a solution for the optimal selection of portfolio drivers as the common drivers. Portfolio constituent dynamics are modeled by Partial Differential Equations, and solutions approximated with neural networks. Sensitivities with respect to the common drivers are obtained via Automatic Adjoint Differentiation. Information on asset dynamics is incorporated via sensitivities into portfolio optimization. Portfolio constituents are embedded into the space of sensitivities with respect to their common drivers, and a distance matrix in this space called the Sensitivity matrix is used to solve the convex optimization for diversification. The sensitivity matrix measures the similarity of the projections of portfolio constituents on a vector space formed by common drivers' returns and is used to optimize for diversification on both idiosyncratic and systematic risks while adding directionality and future behavior information via returns dynamics. For portfolio optimization, we perform hierarchical clustering on the sensitivity matrix. To the best of the author's knowledge, this is the first time that sensitivities' dynamics approximated with neural networks have been used for portfolio optimization. Secondly, that hierarchical clustering on a matrix of sensitivities is used to solve the convex optimization problem and incorporate the hierarchical information of these sensitivities. Thirdly, public and listed variables can be used to obtain maximum idiosyncratic and systematic diversification by means of the sensitivity space with respect to optimal portfolio drivers. We reach over-performance in many experiments with respect to all other out-of-sample methods for different markets and real datasets.
