Modele graniczne w teorii ryzyka ubezpieczeniowego

• Autorzy: Zbigniew Michna

Warianty tytułu

Limit Models in Insurance Risk Theory.

• Języki publikacji: PL

Abstrakty

Przedstawiono różne modele ryzyka, których wybór dla konkretnego ubezpieczyciela ma ogromne znaczenie, gdyż prawdopodobieństwo ruiny znacznie różni się w tych modelach. Są to: model, w którym proces ryzyka jest przybliżany za pomocą ruchu Browna, za pomocą stabilnego ruchu Lévy'ego, model ryzyka dla roszczeń skorelowanych, metodę symulacji prawdopodobieństwa ruiny na nieskończonym horyzoncie czasu w modelu dobrych i złych okresów. Przedstawiono także aproksymacje modeli kolejkowych.

EN

In this paper we consider insurance risk models. We approximate a risk reserve process by Brownian motion, a-stable Levy motion and fractional Brownian motion. These three models cover the cases when claims are small, large and appearing in good and bad periods. We show that self-similarity is an important feature of insurance models. We find bounds and asymptotic behavior of ruin probability on finite and infinite time horizon. We present methods of simulation of ruin probability. We investigate importance sampling method to simulate ruin probability. We simulate ruin probabilities under Polish insurance system conditions. The presented results are extended to queueing systems when interarrivais and service times do not necessary possess the second moment. The given methods and models are applicable in telecommunication and computer systems as well. (original abstract)

Słowa kluczowe

PL

Ryzyko w ubezpieczeniach; Teoria ryzyka; Modelowanie niepewności; Modele stochastyczne; Przegląd literatury

EN

Insurance risk; Theory of risk; Modeling uncertainty; Stochastic models; Literature review

• Czasopismo: Prace Naukowe Akademii Ekonomicznej we Wrocławiu. Seria : Monografie i Opracowania (nr 100)
• Rocznik: 2002
• Numer: nr 962
• Strony: 103

Twórcy

autor

Zbigniew Michna

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