Modelling Dependence in Insurance Claims Processes with Lévy Copulas

ASTIN Bulletin, Vol. 41, No. 2, pp. 575-609

25 Pages Posted: 3 Aug 2011 Last revised: 6 Jan 2012

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

Luke Cameron Cassar

University of New South Wales (UNSW) - School of Actuarial Studies

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Multiple version iconThere are 2 versions of this paper

Date Written: August 3, 2011

Abstract

In this paper we investigate the potential of Lévy copulas as a tool for modelling dependence between compound Poisson processes and their applications in insurance. We analyse characteristics regarding the dependence in frequency and dependence in severity allowed by various Lévy copula models. Through the introduction of new Lévy copulas and comparison with the Clayton Lévy copula, we show that Lévy copulas allow for a great range of dependence structures.

Procedures for analysing the fit of Lévy copula models are illustrated by fitting a number of Lévy copulas to a set of real data from Swiss workers compensation insurance. How to assess the fit of these models with respect to the dependence structure exhibited by the dataset is also discussed.

Finally, we provide a decomposition of the trivariate compound Poisson process and discuss how trivariate Lévy copulas model dependence in this multivariate setting.

Keywords: Lévy Copula, Dependence, Compound Poisson Process, Insurance, Real Data

JEL Classification: G22, C46, C51, C52

Suggested Citation

Avanzi, Benjamin and Cassar, Luke Cameron and Wong, Bernard, Modelling Dependence in Insurance Claims Processes with Lévy Copulas (August 3, 2011). ASTIN Bulletin, Vol. 41, No. 2, pp. 575-609. Available at SSRN: https://ssrn.com/abstract=1904093

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies ( email )

UNSW Sydney, NSW 2052
Australia

Luke Cameron Cassar

University of New South Wales (UNSW) - School of Actuarial Studies ( email )

Sydney, NSW 2052
Australia

Bernard Wong (Contact Author)

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

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