Chernobai, Anna and Burnecki, Krzysztof and Rachev, Svetlozar and Trueck, Stefan and Weron, Rafal (original) (raw)

In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a non-homogeneous Poisson process with a sinusoidal intensity rate function. The choice of an adequate loss distribution is conducted via the in-sample goodness-of-fit procedures and forecasting, using classical and robust methodologies. Modelling catastrophe claims with left-truncated severity distributions Anna Chernobai, Krzysztof Burnecki, Svetlozar Rachev, Stefan Trück and Rafa l Weron University of California Santa Barbara, CA 93106, USA 2 Hugo Steinhaus Center for Stochastic Methods, Institute of Mathematics, Wroc law University of Technology, 50-370 Wroc law, Poland 3 Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, D-76128 Karlsruhe, Germany