The Application of Bühlmann-Straub Model to the Estimation of Net Premium Rates in the Motor Third-Party Liability Insurance of Vehicle Owners

Anna Szymańska

Abstract


One of the elements used in the process of tariff calculation of premiums in motor liability insurance is a bonus-malus system. This systems takes into account the “claims ratio” by means of increases and discounts of the base premium called net premium rates. The aim of this work is to propose an estimation method of the net premium rates in the groups of the motor third-party liability insurance portfolio of individuals. One of the maximum likelihood models, called the Bühlmann-Straub model was used for the premium estimation.


Keywords


credibility theory; Bühlmann-Straub model; bonus-malus system; net premium rates; motor third-party liability insurance

Full Text:

PDF (Język Polski)

References


Bühlmann H., Experience Rating and Credibility, “ASTIN Bulletin” 1967, No. 4 (3).

Bühlmann H., Straub E., Glaubwürdigkeit für Schadensätze, “Mitteilungen der Vereiningung scheizerischer Vesicherungsmathematiker” 1970.

Daykin C.D., Pentiäinen T., Pesonen M., Practical Risk Theory for Actuaries, Chapman & Hall, London 1994.

Denuit M., Marechal X., Pitrebois S., Walhin J.F., Actuarial Modelling of Claim Counts. Risk Classification, Credability and Bonus-Malus Systems, Wiley & Sons, England 2007, DOI: https://doi.org/10.1002/9780470517420.

Jasiulewicz H., Teoria zaufania. Modele aktuarialne, Wydawnictwo AE im. Oskara Langego we Wrocławiu, Wrocław 2005.

Johansson B., Ohlsson E., Non-life Insuranse Pricing with Generalized Lineał Models, Spinger-Verlag, Berlin 2010.

Kaas R., Goovaerts M., Dhaene J., Denuit M., Modern Actuarial Risk Theory, Kluwer, Boston 2001.

Kowalczyk P., Poprawska E., Ronka-Chmielowiec W., Metody aktuarialne, PWN, Warszawa 2006.

Krzyśko M., Statystyka matematyczna, cz. 2, Wydawnictwo Naukowe UAM, Poznań 1997.

Lemaire J., Bonus-malus Systems in Automobile Insurance, Kluwer, Boston 1995, DOI: https://doi.org/10.1007/978-94-011-0631-3.

Ostasiewicz W. (red.), Modele aktuarialne, Wydawnictwo AE im. O. Langego we Wrocławiu, Wrocław 2000.

Szymańska A., Statystyczna analiza systemów bonus-malus w ubezpieczeniach komunikacyjnych, Wydawnictwo UŁ, Łódź 2014.




DOI: http://dx.doi.org/10.17951/h.2016.50.4.497
Date of publication: 2017-02-20 17:31:15
Date of submission: 2016-05-29 12:07:35


Statistics


Total abstract view - 397
Downloads (from 2020-06-17) - PDF (Język Polski) - 0

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Anna Szymańska

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.