Ulepszenie aproksymacji indywidualnego modelu ryzyka przez kolektywny model ryzyka

• Authors: Anna Nikodem-Słowikowska

Title variants

Improving the approximation of individual risk model by the compound risk model

• Languages of publication: PL

Abstracts

EN

In the individual risk model the aggregate claims distribution can be calculated by using the compound distribution. In this article two approximations will be described: the compound Poisson approximation and the compound negative binomial approximation. Using this method of calculated aggregate claims distribution, errors of approximation are made. To reduce these errors the higher order approximations can be used, which are taken from [Pits]. In this article the numerical examples, including the refinement of the compound approximation, are considered for homogeneous portfolio and for inhomogeneous portfolios with two classes.

Keywords

EN

individual risk model; collective risk model; compound Poisson approximation; compound negative binomial approximation; first order approximation

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Śląski Przegląd Statystyczny
• Year: 2012
• Issue: 10(16)
• Pages: 69-81

Dates

published

2012

Contributors

author

Anna Nikodem-Słowikowska

• Uniwersytet Ekonomiczny we Wrocławiu

References

• Daykin C.D., Pentikainen T., Pesonen M., Practical risk Theory for Actuaries, Chapman & Hall, London 1994.
• Feller W., Wstęp do rachunku prawdopodobieństwa, PWN, Warszawa 1969.
• Hipp C., Improved approximations for the aggregate claims distribution in the individual model, ”ASTIN Bulletin” 1986, 16, s. 89-100.
• Kaas R., Goovaerts M., Dhaene J., Denuit M., Modern Actuarial Risk Theory, Kluwer Academic Publishers, Boston 2001.
• Klugman S.A., Panjer H.H., Willmot G.E., Loss Models. From Data to Decision, John Wiley & Sons, New York 1998.
• Michel R., An improved error bound for the compound Poisson approximation of a nearly homogenous portfolio, “ASTIN Bulletin” 1987, 17, no 2, s. 165-169.
• Modele aktuarialne, red. W. Ostasiewicz. Wyd. AE, Wrocław 2000.
• Otto W., Ubezpieczenia majątkowe. Część I. Teoria ryzyka, Wydawnictwo Naukowo-Techniczne, Warszawa 2004.
• Pitts S.M., A functional approach to approximations for the individual risk model, “ASTIN Bulletin” 2004, 34, no 2, s. 379-397.
• Rolski T., Schmidli H.P., Schmidt V., Teugels J., Stochastic Processes for Insurance and Finance, John Wiley & Sons, Chichester 1999.