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EXPECTED PREMIUM IN THE MODEL OF BONUS-MALUS SYSTEM FAIR BY TRANSITION RULES

100%
Podgorska M.
Roczniki Kolegium Analiz Ekonomicznych
|
2008
|
vol. 18
25-41
EN
The subject of the paper are basic properties of bonus-malus system fair by the transition rules between classes (BMSF(TR)), of which definition excludes unrealistic bonus-malus systems. The paper presents an ergodic Markov chain which is a BMSF(TR) model and which allows to analyze the properties of expected value of insurance premium according to the features characterizing an insured and a system i.e. claims frequency, class in the initial year, insurance duration and maximum number of claims acknowledged in the system.
2
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EXTREME TYPES OF BONUS-MALUS SYSTEM FAIR BY TRANSITION RULES

100%
Podgorska M.
Roczniki Kolegium Analiz Ekonomicznych
|
2008
|
vol. 18
43-68
EN
In the article four extreme variants of BMSF(TR) in which extreme transition rules are valid, i.e. rules of maximum/minimum advancement and maximum/minimum fall, are presented. These four systems allow us to determine the lowest and highest expected premium in any insurance year in any BMSF(TR) and the intervals of values of expected premium in the systems of BMSF(TR) type which are modifications of these four extreme systems.
3
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Statystyczna analiza wyników testu koniunktury

100%
Podgorska M.
Prace i Materiały Instytutu Rozwoju Gospodarczego SGH
|
1998
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vol. 60
65-88
EN
Results of business activity tests are characterized by very strong structural variation. Complex, multidimensional structure of population of enterprises being considered is the main source of diversity. Dynamic approach introduces periodical variation in values of certain variables, intensity of observed processes, and quality of ex post predictions. For instance, in construction industry, one factor which introduces the largest variation is the criterion of ownership. Also for industrial enterprises and trading companies, the largest differences are observed between groups of public sector and private sector enterprises. For the purpose of analysis of business activity tests results, traditional statistical methods may be used. In this chapter we introduce point estimators and interwal estimators of balances and business activity indicators. We consider the problem of aggregation of balances and define distribution of aggregated balances and its main moments. We present a construction of a significance test with test statistics A which has asymptotically normal distribution. The test measures significance of differences of business activity indicators between selected structural groups. We list assumptions necessary to obtain probability distributions of appropriate variables and show the most important properties of these distributions. Applications of proposed statistical analysis methods are described using construction industry activity data for Poland and Italy. As an example of conclusions drawn for Poland, we found strong correlation between assessments of business activity and sociopolitical conditions, as well as unfair treatment of different groups of business enterprises by central administration. Analysis of seasonal variation of construction industry activity confirmed legitimacy of assumed business activity indicator. It is a leading indicator which precedes changes in economic situation by about 3 months. Results of business activity tests for Italian industry do not confirm existence of significant seasonal variation of business activity. Results aggregated over 30 years of conducting tests in Italy clearly indicate that in construction industry, unfavorable periods outnumber favorable ones.
4
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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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