论文标题
通过机器学习和Lie组的SDE进行评估过渡建模的新型方法
A novel approach to rating transition modelling via Machine Learning and SDEs on Lie groups
论文作者
论文摘要
在本文中，我们引入了一种新型方法，以模拟使用随机过程的额定值过渡。为了引入随机过程，其值是有效的级矩阵，我们注意到随机矩阵的几何特性及其与矩阵谎言组的链接。我们对该主题进行温和的介绍，并演示R中的ITô-Sdes如何为评级过渡产生所需的模型。为了将评级模型校准为历史数据，我们使用称为TimeGAN的深神经网络（DNN）来学习历史评级矩阵的时间序列的特征。然后，我们使用此DNN生成合成评级过渡矩阵。之后，我们在特定时间点适合生成的评级矩阵和评级过程的时刻，从而拟合得很好。校准后，我们通过检查一些额定时间序列应满足的属性来讨论校准的额定过渡过程的质量，并且我们将看到这种几何方法效果很好。
In this paper, we introduce a novel methodology to model rating transitions with a stochastic process. To introduce stochastic processes, whose values are valid rating matrices, we noticed the geometric properties of stochastic matrices and its link to matrix Lie groups. We give a gentle introduction to this topic and demonstrate how Itô-SDEs in R will generate the desired model for rating transitions. To calibrate the rating model to historical data, we use a Deep-Neural-Network (DNN) called TimeGAN to learn the features of a time series of historical rating matrices. Then, we use this DNN to generate synthetic rating transition matrices. Afterwards, we fit the moments of the generated rating matrices and the rating process at specific time points, which results in a good fit. After calibration, we discuss the quality of the calibrated rating transition process by examining some properties that a time series of rating matrices should satisfy, and we will see that this geometric approach works very well.
