On dynamic credibility models

• Authors: Ferenstein Elżbieta

Title variants

PL

O dynamicznych modelach wiarygodności

• Languages of publication: EN

Abstracts

EN

The Bühlamnn-Straub credibility model is extended for risk profiles varying with time. This is a special case of an evolutionary credibility model with risk parameter changing with time according to an unobserved sequence of random variables. The exact formulas of Bayes premiums are obtained for models in which the probability distributions of risk profiles switch to others at random unobserved time periods with known distributions. In particular, for exponential type class of distributions with conjugate priors, the Bayes premium is obtained recursively from a non-linear multidimensional Kalman type filter.

PL

Model Bühlmanna-Strauba rozszerzono o profile ryzyka zmieniające się z czasem. Jest to szczególny przypadek ewolucyjnego modelu wiarygodności ze zmiennym w czasie parametrem ryzyka zależnym od nieobserwowanego ciągu zmiennych losowych. Otrzymano dokładną postać składek bayesowskich dla modeli, w których rozkłady prawdopodobieństwa profili ryzyka zmieniają się w nieobserwowanych losowych momentach o znanych rozkładach. Przede wszystkim dla wykładniczych klas rozkładów ze sprzężonymi rozkładami a priori otrzymano składkę bayesowską rekurencyjnie jako pewien nieliniowy wielowymiarowy filtr Kalmana.

Keywords

EN

Bayes premium; Bühlmann-Straub model; credibility model; exponential dispersion models; dispersion distribution; conjugate priors

PL

składka bayesowska; model Bühlmanna-Strauba; model wiarygodności; dyspersyjne modele wykładnicze; sprzężone rozkłady a priori

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Śląski Przegląd Statystyczny
• Year: 2020
• Issue: 18 (24)
• Pages: 133-148

Contributors

author

Ferenstein Elżbieta

• Warsaw University of Technology, Poland

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