Advanced Dependence Modeling of Loss Reserves: Integrating Recurrent Neural Networks and Seemingly Unrelated Regression Copula Mixed Models for Diversified Risk Capital

Abstract

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. The actuarial industry has developed both parametric and non-parametric methods for 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 thesis 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. Further, 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. We refer to the integration of DT for multivariate loss reserving and GAN for risk capital analysis as the extended Deep Triangle (EDT). As the second contribution of this thesis, we propose SUR copula mixed models to enhance SUR copula regression with multiple companies' data for loss prediction and risk capital analysis. Due to the heterogeneous history of losses between companies and different LOBs, we model this heterogeneity using random effects and select varying distributions for losses from each LOB. We model the development and accident year effects as fixed effects and apply shrinkage to make it more robust to the decreasing number of observations over accident year and development year. To illustrate EDT and SUR copula mixed models, we apply and calibrate these methods using data from multiple companies from the National Association of Insurance Commissioners database. For validation, we compare the EDT and SUR copula mixed model to the SUR copula regression models and find that the EDT and SUR copula mixed model outperform the SUR copula regression models in predicting total loss reserve. Furthermore, with the obtained predictive distribution for reserves, we show that risk capital calculated from the EDT and SUR copula mixed model is smaller than that of the SUR copula regression models, suggesting a more considerable diversification benefit. We also confirmed these findings in simulation studies. Finally, we introduce a chapter on a hybrid semi-parametric approach, which bridges the interpretability of dependence structures with the flexibility to capture complex effects, including interactions; its deeper application and simulation studies are left for future work.