Fair Bonus-Malus Systems

• Autorzy: Maria Podgórska , Barbara Kryszeń , Małgorzata Niemiec
• Języki publikacji: EN

Abstrakty

EN

In spite of over 50 years of existence of a bonus-malus system (BMS) many crucial problems concerning its modelling, analysis and optimisation remain unsolved. Definitions of BMS proposed in literature are so general that they include systems which could not exist and perform well in the competitive automobile insurance, market, and therefore they are not used in practice. The objective of this article is to present two definitions of fair bonus-malus systems, which differ in the criterion of distinguishing BMS, however both allow for eliminating systems with non-realistic structures. The first proposal is the definition of so called bonus-malus system fair by premium (BMSFpx). The concept of this system consists in excluding from considerations such systems, in which policyholders are penalized with the greater premium after reporting fewer losses or after claiming a given number of losses if they were in better class. The criterion for distinguishing BMS in the second definition is based on the transition rules i.e. rules governing the transition of the insured, having reported a given number of claims, from one class to another. Therefore, these systems are namedfair bonus-malus sys-tems by transition rules (BMSFTIt). In this paper it is also proved that each BMSFTR is also BMSFPR. (original abstract)

Słowa kluczowe

EN

Motor insurance; Single market for insurance; Bonus-malus system

PL

Ubezpieczenia komunikacyjne OC; Jednolity rynek ubezpieczeniowy; Systemy bonus-malus

• Czasopismo: Roczniki Kolegium Analiz Ekonomicznych / Szkoła Główna Handlowa
• Rocznik: 2008
• Numer: nr 18 Modelling and analysis of automobile insurance and financial markets
• Strony: 11--24

Twórcy

autor

Maria Podgórska

• Szkoła Główna Handlowa w Warszawie

autor

Barbara Kryszeń

autor

Małgorzata Niemiec

• Szkoła Główna Handlowa w Warszawie

Bibliografia

• Cieślik B. (2003), Comparative analysis of bonus-malus systems in Poland (in Polish), Institute of Econometrics, Warsaw School of Economics, Warsaw.
• Kryszeń B. (2005a), Expected insurance premium in bonus-malus system as a non-decreasing function of claim frequency (in Polish), Annals of Collegium of Economic Analyses, Volume 14, pp. 45-57.
• Kryszeń B. (2005b), The claims number distribution modelling in the non- homogenous motor insurance portfolio (Ph. D. thesis in Polish), Collegium of Economic Analyses, Warsaw School of Economics, Warsaw.
• Lemaire J. (1995), Bonus-Malus Systems in Automobile Insurance, Kluwer Academic Publishers, Boston.
• Niemiec M. (2007), Matrix of mean first passage and return time in the analysis of a bonus-malus system (Ph.D. thesis in Polish), Collegium of Economic Analyses, Warsaw School of Economics, Warsaw.
• Podgórska M., (2008), Fair bonus-malus system in the sense of transitions between classes (in Polish), in: Actuarial Statistics - theory and applications, Wrocław, pp. 206-231.
• Podgórska M., Cieślik B, Kryszeń B., Niemiec M., Topolewski M. (2006), Fair bonus-malus system in the sense of transitions between classes (in Polish), Institute of Econometrics, Warsaw School of Economics, Warsaw.