Credibility Using Copulas

Edward Frees and Ping Wang

North American Actuarial Journal, 2005, vol. 9, issue 2, 31-48

Abstract: Credibility is a form of insurance pricing that is widely used, particularly in North America. The theory of credibility has been called a “cornerstone” in the field of actuarial science. Students of the North American actuarial bodies also study loss distributions, the process of statistical inference of relating a set of data to a theoretical (loss) distribution. In this work, we develop a direct link between credibility and loss distributions through the notion of a copula, a tool for understanding relationships among multivariate outcomes.This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross section of risk classes (towns) with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time; specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution; like the univariate tdistributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.We present an illustrative example of Massachusetts automobile claims, and compare our new credibility estimates with those currently existing in the literature.

Date: 2005
References: Add references at CitEc
Citations: View citations in EconPapers (28)

Downloads: (external link)
http://hdl.handle.net/10.1080/10920277.2005.10596196 (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:9:y:2005:i:2:p:31-48

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

DOI: 10.1080/10920277.2005.10596196

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 ().