A Set of Bonus-Malus Systems Fair by Transitions Rules - Elements of Analysis
Treść / Zawartość
The paper considers a set of bonus-malus systems fair by transition rules (BMSFTR). Al-though the definition of such system reduces a set of all BM systems, the number of systems of BMSFTR type still remains huge First we use a special algorithm to generate all possible systems of BMSFTR type with a given number of classes. Then we propose to implement a premium criterion that fulfils the definition of BMSFTR and, which is very important, makes systems financially balanced. Next we choose appropriate measures which allow to analyse and compare all possible systems of a given size in respect of their performance in different portfolios i.e. portfolios which differ by claim frequency and claim variance. The results of the analysis are general conclusions on how transition rules and portfolio's characteristics influence system performance. (original abstract)
- Borgan ., Hoem J.M., Norberg R. (1981), ANonasymptotic Criterion for Evaluation of Automobile Bonus Systems, Scandinavian Actuarial Journal, s.165-178.
- Cieślik B. (2003), Comparative analysis of bonus-malus systems in Poland (in Polish), Institute of Econometrics, Warsaw School of Economics, Warsaw.
- Lemaire J. (1995), Bonus-malus Systems in Automobile Insurance, Kluwer Nijhoff, Boston.
- LoimarantaK. (1972), Some Asymptotic Properties of Bonus Systems, ASTIN BULLETIN, Vol. VI, Part 3, pp. 233-245.
- Niemiec M. (2004), Mean first passage times matrix in the bonus-malus system analysis (in Polish); in: Quantitative methods in economics, Oficyna Wydawnicza SGH, Warsaw.
- Niemiec M. (2007), Matrix of mean first passage and return times in the bonus- malus system analysis (Ph.D. thesis in Polish); Collegium of Economic Analyses, Warsaw School of Economics, Warsaw.
- Norberg R. (1976), A credibility theory for automobile bonus systems, Scandinavian Actuarial Journal, pp. 92-107.
- 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.
- Podgórska M., Kryszeń B, Niemiec M. (2008), Fair bonus-malus systems, Annals of Collegium of Economic Analyses, Volume 18, pp.
- Willmot G. E. (1987), The Poisson-Inverse Gaussian Distribution as an Alternative to Negative Binominal, Scandinavian Actuarial Journal, pp. 113-127.