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Risks 2014, 2(1), 49-73; doi:10.3390/risks2010049
Article

Modeling and Performance of Bonus-Malus Systems: Stationarity versus Age-Correction

Received: 30 September 2013; in revised form: 17 February 2014 / Accepted: 18 February 2014 / Published: 11 March 2014
(This article belongs to the Special Issue Application of Stochastic Processes in Insurance)
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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.
Keywords: actuarial mathematics; Bayes premium; equilibrium distribution; experience rating; insurance portfolio; Markov chain; motor insurance; Poisson claims; stationary distribution actuarial mathematics; Bayes premium; equilibrium distribution; experience rating; insurance portfolio; Markov chain; motor insurance; Poisson claims; stationary distribution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Asmussen, S. Modeling and Performance of Bonus-Malus Systems: Stationarity versus Age-Correction. Risks 2014, 2, 49-73.

AMA Style

Asmussen S. Modeling and Performance of Bonus-Malus Systems: Stationarity versus Age-Correction. Risks. 2014; 2(1):49-73.

Chicago/Turabian Style

Asmussen, Søren. 2014. "Modeling and Performance of Bonus-Malus Systems: Stationarity versus Age-Correction." Risks 2, no. 1: 49-73.


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