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STATIONARY PROPERTIES OF EXTREME BONUS-MALUS SYSTEMS FAIR BY TRANSITION RULES

100%
Niemiec M.
Roczniki Kolegium Analiz Ekonomicznych
|
2008
|
vol. 18
69-81
EN
The purpose of this paper is to present stationary properties of four 'extreme' cases of bonus-malus systems fair by transition rules, characterized by rules of maximum/minimum advancement and maximum/minimum fall in each class. General formulae for the stationary distributions and mean stationary premiums for these systems are derived. Also the first attempt to define the impact of a change in the number of classes on the values of mean stationary premium has been made.
2
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A SET OF BONUS-MALUS SYSTEMS FAIR BY TRANSITION RULES - ELEMENTS OF ANALYSIS

63%
Niemiec M., Topolewski M.
Roczniki Kolegium Analiz Ekonomicznych
|
2008
|
vol. 18
113-145
EN
The paper considers a set of bonus-malus systems fair by transition rules (BMSF(TR)). Although the definition of such system reduces a set of all BM systems, the number of systems of BMSF(TR) type still remains huge. First the authors use a special algorithm to generate all possible systems of BMSF(TR) type with a given number of classes. Then they propose to implement a premium criterion that fulfils the definition of BMSF(TR) and, which is very important, makes systems financially balanced. Next they 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.
3
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FAIR BONUS-MALUS SYSTEMS

51%
Podgorska M., Kryszen B., Niemiec M.
Roczniki Kolegium Analiz Ekonomicznych
|
2008
|
vol. 18
11-24
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 (BMSF(PR)). 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 named fair bonus-malus systems by transition rules (BMSF(TR)). In this paper it is also proved that each BMSF(TR) is also BMSF(PR)
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