Credibility estimation in insurance data: generalized linear models and evolutionary modeling
FacultiesFakultät für Mathematik und Wirtschaftswissenschaften
Generalized linear models (GLM) have multiple applications, in particular they are a popular tool in insurance for fitting claims data. Insurance portfolios typically consist of heterogeneous clusters with similar but different risk characteristics. Problems arise when only limited statistical information is available for individual clusters. Credibility theory is a commonly used actuarial tool to improve statistical inference for small clusters, however credibility estimators have only been developed for a few specific models and a general theory remains lacking. In the present thesis we fill that gap, presenting a credibility estimator in a general GLM setting allowing all simple exponential families with natural link functions and cluster specific volume parameters. We study asymptotic properties of the estimator and illustrate our new concept with both a simulation study and an application to mortality data. In the second part of the thesis we deal with an application of evolutionary credibility models to mortality data. Such a model correctly recognizes the random nature of the underlying time factor and further allows for the flexibility of time series modeling. The final model incorporates a smoothing procedure over time that ensures robustness over successive forecasts.
Subject HeadingsAsymptotik [GND]
Verallgemeinertes lineares Modell [GND]
Asymptotic theory [LCSH]
Credibility theory (Insurance) [LCSH]