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Modeling and Performance of Bonus-Malus Systems: Stationarity versus Age-Correction
- Source :
- Risks, Vol 2, Iss 1, Pp 49-73 (2014), Risks; Volume 2; Issue 1; Pages: 49-73, Asmussen, S 2013 ' Modeling and performance of Bonus-Malus Systems: Stationarity versus age-correction ' T.N. Thiele Centre, Department of Mathematics, Aarhus University .
- Publication Year :
- 2014
- Publisher :
- MDPI AG, 2014.
-
Abstract
- In a bonus-malus system in car insurance, the bonus class of a customer is updated from one year to the next as a function of the current class and the number of claims in the year (assumed Poisson). Thus the sequence of classes of a customer in consecutive years forms a Markov chain, and most of the literature measures performance of the system in terms of the stationary characteristics of this Markov chain. However, the rate of convergence to stationarity may be slow in comparison to the typical sojourn time of a customer in the portfolio. We suggest an age-correction to the stationary distribution and present an extensive numerical study of its effects. An important feature of the modeling is a Bayesian view, where the Poisson rate according to which claims are generated for a customer is the outcome of a random variable specific to the customer.
- Subjects :
- Strategy and Management
Economics, Econometrics and Finance (miscellaneous)
Bayesian probability
Markov chain
motor insurance
jel:C
Poisson distribution
lcsh:HG8011-9999
actuarial mathematics
Bayes premium
equilibrium distribution
experience rating
insurance portfolio
Poisson claims
stationary distribution
lcsh:Insurance
jel:M4
jel:K2
symbols.namesake
jel:G0
jel:G1
jel:G2
Accounting
jel:G3
ddc:330
Econometrics
Bonus-malus
Actuarial science
Stationary distribution
Outcome (probability)
jel:M2
Rate of convergence
symbols
Business
Random variable
Subjects
Details
- Language :
- English
- ISSN :
- 22279091
- Volume :
- 2
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Risks
- Accession number :
- edsair.doi.dedup.....1bd3cfa743cb66c12b9116c83fa816ad