Modele zależności w agregacji ryzyka ubezpieczyciela

• Autorzy: Stanisław Wanat

Warianty tytułu

Dependence Models in the Aggregating of Insurer Risks

• Języki publikacji: PL

Abstrakty

Celem niniejszej pracy jest prezentacja metod modelowania zależności i ich wykorzystania w kontekście agregacji ryzyka w działalności ubezpieczeniowej, przy czym uwaga jest skoncentrowana nie tylko na ryzyku ubezpieczeniowym, ale także na ryzyku związanym z funkcjonowaniem zakładu ubezpieczeń. Przedstawiane w niej metody modelowania zależności można zaliczyć głównie do ostatniego z wyżej wymienionych nurtów, czyli wykorzystującego rozkłady wielowymiarowe, oraz pierwszego, w którym zależność uwzględniana jest przez wprowadzanie interakcji w modelach opisujących liczbę szkód. Problem agregacji ryzyka w ubezpieczeniach i ściśle z nim związane metody modelowania zależności stają się obecnie niezmiernie ważne, głównie za sprawą rozwiązań proponowanych w systemie Solvency II dotyczących kompleksowej oceny ryzyka ubezpieczyciela. Wiadomo, że zakłady ubezpieczeń zarządzają kapitałami, które odnoszą się do szerokiego zakresu różnych produktów ubezpieczeniowych zgrupowanych w portfele ubezpieczeń i linie biznesu (grupy ubezpieczeń), ponadto ich działalność narażona jest na ryzyko charakterystyczne dla rynku finansowego i ryzyko systematyczne związane z funkcjonowaniem gospodarki. W związku z tym kompleksowy model ryzyka ubezpieczyciela wymaga połączenia modeli opisujących ryzyko w obrębie ustalonego tzw. poziomu agregacji, tj. poziomu pojedynczej polisy (kontraktu), poziomu portfela ubezpieczeń, poziomu linii biznesu (grupy ubezpieczeń) i poziomu zakładu ubezpieczeń, jak również połączenia modeli ryzyka z różnych poziomów. Przy takim podejściu wymogi kapitałowe związane z całkowitym ryzykiem ubezpieczyciela wyznacza się na drodze agregacji wymogów kapitałowych z tytułu rozpoznanych czynników ryzyka, na które jest on narażony. (fragment tekstu)

EN

A fundamental yet difficult responsibility an insurance company has in managing / risk is properly identifying, quantifying and aggregating those risk factors that influence its operations. In the subject literature, a great deal of work has been devoted to methods of identifying, classifying and quantifying the risks insurers face, while relatively little has been written about the issue of aggregating risks in insurance or the dependence between risks, which is inextricably linked to aggregation. These issues are becoming exceedingly important, mainly in terms of measures for insurer risk proposed in the Solvency II system. According to these measures, the insurer designates the capital require- ments for the insurer's overall risk in the process of aggregating the capital requirements on the grounds of recognised risk factors. The present monograph is one of the first attempts in the Polish literature to present fa complex approach to the issue of aggregating risks in insurance and problems in modeling dependencies that accompany this process. It may become a source of knowledge on both the methods for describing, measuring and modeling different types of dependence and tools that enable these methods to be used in the process of aggregating insurer risks. The first chapter presents the issue of aggregating risks in insurance activity and the importance of problems in properly recognising the dependence between risks. The second chapter presents the existing concepts of stochastic dependence between random variables, their notation in the language of probability as well as methods for comparing the "strength" of dependence and its expression with the help of dependence measures. The third chapter presents the copula function as a tool which enables a wide range of dependence structures to be considered in the modeling of multi-dimensional distribution of risk variables. The fourth chapter presents methods for considering available information on the dependence structure in the process of aggregating risks. The fifth chapter presents selected methods of implementing" structural dependencies into the modeling of insurer risk. The sixth chapter looks at how to properly recognise the dependence structures in calculating the solvency capital requirements in the context of the Solvency II system. (short original abstract)

Słowa kluczowe

PL

Ubezpieczenia; Ryzyko w ubezpieczeniach; Zarządzanie ryzykiem; Statystyka matematyczna; Zmienne losowe; Rozprawa habilitacyjna

EN

Insurances; Insurance risk; Risk management; Mathematical statistics; Random variable; Habilitation thesis

• Czasopismo: Zeszyty Naukowe / Uniwersytet Ekonomiczny w Krakowie. Seria Specjalna, Monografie
• Rocznik: 2012
• Numer: nr 211
• Strony: 215

Twórcy

autor

Stanisław Wanat

• Uniwersytet Ekonomiczny w Krakowie

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