Reserves comprise most of the liabilities of a property and casualty (P&C) company and are actuaries' best estimate for unpaid future claims. Notably, the reserves for different lines of business (LOB) are related, as there may be dependence between events related to claims. There have been parametric and non-parametric methods in the actuarial industry for loss reserving; only a few tools have been developed to use the recurrent neural network (RNN) for multivariate loss reserving and risk capital analyses. This paper aims to study RNN methods to model dependence between loss triangles and develop predictive distribution for reserves using machine learning. Thus, we create an RNN model to capture dependence between LOBs by extending the Deep Triangle (DT) model from Kuo (2019). In the extended Deep Triangle (EDT), we use the incremental paid loss from two LOBs as input and the symmetric squared loss of two LOBs as the loss function. Then, we extend generative adversarial networks (GANs) by transforming the two loss triangles into a tabular format and generating synthetic loss triangles to obtain the predictive distribution for reserves. To illustrate our method, we apply and calibrate these methods on personal and commercial automobile lines from a large US P&C insurance company and compare the results with copula regression models. The results show that the EDT model performs better than the copula regression models in predicting total loss reserve. In addition, with the obtained predictive distribution for reserves, we show that risk capitals calculated from EDT combined with GAN are smaller than that of the copula regression models, which implies a more considerable diversification benefit. Finally, these findings are also confirmed in a simulation study.

翻译：准备金构成财产与意外险公司负债的主要部分，是精算师对未支付未来索赔的最佳估计。值得注意的是，不同业务线的准备金相互关联，因为与索赔相关的事件之间可能存在依赖关系。精算行业已存在多种参数化与非参数化的损失准备金方法，但仅有少数工具采用循环神经网络进行多变量损失准备金与风险资本分析。本文旨在研究利用循环神经网络方法对损失三角之间的依赖关系建模，并通过机器学习开发准备金的预测分布。为此，我们通过扩展Kuo（2019）提出的深度三角模型，构建了一个用于捕捉业务线间依赖关系的循环神经网络模型。在扩展深度三角模型中，我们以两条业务线的增量已付损失作为输入，并将两条业务线的对称平方损失作为损失函数。随后，我们通过将两个损失三角转换为表格格式并生成合成损失三角，扩展生成对抗网络以获得准备金的预测分布。为阐明我们的方法，我们将这些方法应用于美国一家大型财产与意外险公司的个人与商业汽车保险业务线并进行校准，同时将结果与Copula回归模型进行比较。结果表明，扩展深度三角模型在预测总损失准备金方面优于Copula回归模型。此外，基于所得准备金预测分布，我们发现扩展深度三角模型结合生成对抗网络计算出的风险资本低于Copula回归模型，这表明具有更显著的风险分散效应。最后，模拟研究也证实了这些发现。