Advanced Claims Reserving Methods

In the first part of this thesis, theoretical background as well as practical application of generalized linear mixed models (GLMM) and generalized estimation equations (GEE) as an extensions of GLM for estimation of the loss reserves are shown. Both of these approaches are able to deal with correlated dependent variable, which is the key extension of commonly used methods. Since the GLMM allows incorporating a random effect instead of several fixed effects corresponding to the accident years as in the case of the GLM, volatility of the prediction is reduced. This allows more flexible risk valuation, which is a crucial element of the risk management and the capital allocation practices of non-life insurers. Theory part describes statistical background together with the design of the models suitable for the underlying insurance data. Subsequently, practical application is dedicated to the objective model selection based on residual diagnostics and emphasizes precision of prediction as well as desirable features of the GLMM model proposed by the author in comparison to other methods including Mack chain ladder.Nevertheless, these approaches are based on aggregated data where certain amount of the available information is lost. Therefore, this thesis proposes new approach based on innovative methods utilizing non-aggregated data. Proposed approach for incurred but not reported (IBNR) number of claims combines advanced survival analysis for right truncated and censored data with maximum likelihood or moment estimator. Moreover, severity component of the model employs neural networks or hurdle models. This approach is based on more detailed data so technically more information is utilized. On the other hand non-aggregated data are more volatile so certain loss of robustness may be encountered. A real data example together with diagnostics for the model selection as well as back testing and a bootstrap experiment (simulation study) are provided as an illustration of the potential benefits of the presented approaches.