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. The actuarial industry and literature have extensively developed both parametric and nonparametric methods to model dependence in loss reserving. However, the use of machine learning tools to capture dependence between loss reserves from multiple LOBs and calculate the aggregated risk capital remains uncharted. This article introduces the use of the Deep Triangle (DT), a recurrent neural network, for multivariate loss reserving, incorporating an asymmetric loss function to combine incremental paid losses of multiple LOBs. The input and output to the DT are the vectors of sequences of incremental paid losses that account for the dependence between and within LOBs. In addition, we utilize generative adversarial networks (GANs) to generate synthetic loss triangles, enabling us to obtain the predictive distribution for reserves and calculate the risk capital. We call the combination of DT for multivariate loss reserving and GAN for risk capital analysis the Extended Deep Triangle (EDT). To speed up the training for DT in EDT, we leverage the DT trained on real data. To illustrate the EDT, we apply and calibrate these methods using data from multiple companies from the National Association of Insurance Commissioners (NAIC) database. To benchmark our method, we compare the EDT to the copula regression models and find that the EDT 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 the 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. Our analysis demonstrates the potential of the EDT in predicting loss reserves and conducting risk capital analysis in practice.

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