Claim Reserving: Classical versus Machine Learning Methods

Abstract

In this thesis, we investigate loss reserving with classical methods and deep learning approach. Claim reserving is a crucial task in non-life insurance. Insurance companies have historical data on claim amounts. These data are usually aggregated to loss triangles, which can be analyzed to predict the claim reserve. The reserves for different business lines are related and a copula regression model can link the claims of different business lines. We apply the models on real data and obtain both reserve estimates and risk capitals. Product copula, Gaussian copula, Frank copula and Student’s t copula are used to model the dependence of the two business lines. The AIC of Student’s t copula model is 1.3 percent smaller than the AIC of the Gaussian copula model. The AIC of Frank copula model and Product copula model is within 0.9 percent of the Gaussian copula model’s AIC. The Gaussian copula model generates the largest risk capital gain among all the copula models. Neural networks are popular machine learning methods and have been applied to the loss reserving problem. The DeepTriangle model is a deep learning framework for forecasting paid losses. At each accident year and development year for which we have data, we predict future losses based on observed history. Each training and testing sample is associated with an accident year - development year pair. The input for the training and testing sample is the observed incremental paid loss and claims outstanding as of the accident - development year pair. To capture the dependency between two lines of business, we use the incremental paid loss from two business lines as input to the deep triangle model. The incremental paid loss from the personal auto line and the incremental paid loss from the commercial auto line correspond to the first and the second component of the sample. The predicted reserve from the deep triangle model is within two percent, three percent and nine percent of the predictions from the Gaussian copula, Frank copula and Student’s t copula models, respectively.