Recurrent Neural Networks for Multivariate Loss Reserving and Risk Capital Analysis

In the property and casualty (P&C) insurance industry, reserves comprise most of a company's liabilities. These reserves are the best estimates made by actuaries for future unpaid claims. Notably, reserves for different lines of business (LOBs) are related due to dependent events or claims. While the actuarial industry has developed both parametric and non-parametric methods for loss reserving, only a few tools have been developed to capture dependence between loss reserves. This paper introduces the use of recurrent neural network (RNN) methods for loss reserving domain to model pairwise dependence and time dependence of incremental payments and generate predictive distributions for reserves. We construct an RNN model to capture the complex dependencies between LOBs by expanding the Deep Triangle (DT) model from Kuo (2019) for one LOB. We then 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. The proposed method, which involves building a predictive distribution for the reserve along with the DT model, is called the extended Deep Triangle (EDT). To illustrate EDT, we apply and calibrate these methods using data from 30 companies from the National Association of Insurance Commissioners database (Meyers and Shi, 2011) and compare the results with copula regression models. The findings indicate that the EDT model outperforms the copula regression models in predicting total loss reserve. Furthermore, with the obtained predictive distribution for reserves, we show that risk capitals calculated from EDT are smaller than that of the copula regression models, suggesting a more considerable diversification benefit. Finally, these findings are also confirmed in a simulation study.