On bootstrap estimators of some prediction accuracy measures of loss reserves in a non-life insurance company

Abstract

This article considers the hierarchical generalized linear model (HGLM) for loss reserving in a non-life insurance. In the current insurance practice, insurance companies use generalized linear models (GLM) for prediction of the total loss reserve. This model, however, requires the assumption of independence of random variables occurring in the loss triangle, which may not always be fulfilled. The remedy to this problem is to introduce random effects to the GLM allowing modeling dependence inside the loss triangle. A limitation in the use of HGLM to predict the total loss reserve is the fact that the error of prediction is expressed by a complex analytical formula. An alternative to the analytical approach is to use the bootstrap technique. The main purpose of this article is to propose the full residual and parametric bootstrap procedures for the estimation of three types of prediction accuracy measures. The first is a classic root mean squared error of prediction (RMSE). The second is a quantile of the absolute prediction error (QAPE). The third one, we propose, is a quantile of a mixture of absolute prediction errors. Stochastic properties of the estimators of the accuracy measures are studied in two Monte Carlo simulation experiments. Bootstrap procedures and Monte Carlo simulation are implemented in R program.