Bonus-Malus Systems with Two-Component Mixture Models Arising from Different Parametric Families

George Tzougas, Spyridon Vrontos and Nicholas Frangos

North American Actuarial Journal, 2018, vol. 22, issue 1, 55-91

Abstract: Two-component mixture distributions defined so that the component distributions do not necessarily arise from the same parametric family are employed for the construction of Optimal Bonus-Malus Systems (BMSs) with frequency and severity components. The proposed modeling framework is used for the first time in actuarial literature research and includes an abundance of alternative model choices to be considered by insurance companies when deciding on their Bonus-Malus pricing strategies. Furthermore, we advance one step further by assuming that all the parameters and mixing probabilities of the two component mixture distributions are modeled in terms of covariates. Applying Bayes' theorem we derive optimal BMSs either by updating the posterior probability of the policyholders’ classes of risk or by updating the posterior mean and the posterior variance. The resulting tailor-made premiums are calculated via the expected value and variance principles and are compared to those based only on the a posteriori criteria. The use of the variance principle in a Bonus-Malus ratemaking scheme in a way that takes into consideration both the number and the costs of claims based on both the a priori and the a posterior classification criteria has not yet been proposed and can alter the resulting premiums significantly, providing the actuary with useful alternative tariff structures.

Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://hdl.handle.net/10.1080/10920277.2017.1368398 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:uaajxx:v:22:y:2018:i:1:p:55-91

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/uaaj20

DOI: 10.1080/10920277.2017.1368398

Access Statistics for this article

North American Actuarial Journal is currently edited by Kathryn Baker

More articles in North American Actuarial Journal from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().