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Odporność składki kwantylowej na ε-zaburzenie rozkładu liczby szkód

Author

Listed:
  • Agata Boratyńska

    (Szkoła Główna Handlowa w Warszawie)

  • Krzysztof Kondraszuk

    (Szkoła Główna Handlowa w Warszawie)

Abstract

W pracy rozważana jest odporność składki kwantylowej w modelu ryzyka łącznego ze względu na zaburzenia rozkładu liczby szkód. Przy obliczaniu składki kwantylowej zostały wykorzystane popularne metody aproksymacji- rozkładem normalnym, przesuniętym rozkładem gamma, przybliżonymi formułami Wilsona-Hilferty’ego oraz Fishera-Cornisha (znanymi w literaturze także jako aproksymacje NP2 oraz NP3), przesuniętym rozkładem odwrotnym gaussowskim oraz aproksymacja mieszana. Jako miarę odporności zastosowano prawdopodobieństwo przekroczenia składki przez łączną szkodę. W artykule przedstawione są wyniki przeprowadzonej analizy dokładności składki kwantylowej przy zaburzaniu rozkładu liczby szkód dla portfela ubezpieczyciela opisanego rozkładami złożonymi- Poissona oraz ujemnym dwumianowym. Odstępstwo od założonego w modelu rozkładu liczby szkód definiuje się w formie ε-zaburzenia. W przeprowadzonym badaniu, które zostało wykonane z wykorzystaniem metod symulacyjnych, uwzględniono analizę wrażliwości składki w zależności od przyjętego rozkładu zaburzającego oraz jego wariancji, siły zaburzenia ε, rozkładu wielkości pojedynczej szkody, jego charakterystyk, a także wielkości portfela.

Suggested Citation

  • Agata Boratyńska & Krzysztof Kondraszuk, 2013. "Odporność składki kwantylowej na ε-zaburzenie rozkładu liczby szkód," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 117-136.
    • Handle: RePEc:sgh:annals:i:31:y:2013:p:117-136
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    References listed on IDEAS

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