Capturing Non-Exchangeable Dependence in Multivariate Loss Processes with Nested Archimedean Lévy Copulas

Forthcoming in Annals of Actuarial Science (2015)

UNSW Australian School of Business Research Paper No. 2014ACTL05

32 Pages Posted: 4 Jul 2014 Last revised: 28 Sep 2015

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

Jamie Tao

Westpac Bank; UNSW Business School

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Xinda Yang

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

Date Written: June 30, 2014

Abstract

The class of spectrally positive Lévy processes is a frequent choice for modelling loss processes in areas such as insurance or operational risk. Dependence between such processes (for example, between different lines of business) can be modelled with Lévy copulas. This approach is a parsimonious, efficient, and flexible method which provides many of the advantages akin to distributional copulas for random variables.

Literature on Lévy copulas seems to have primarily focused on bivariate processes. When multivariate settings are considered, these usually exhibit an exchangeable dependence structure (whereby all subset of the processes have an identical marginal Lévy copula).

In reality, losses are not always associated in an identical way, and models allowing for non-exchangeable dependence patterns are needed. In this paper, we present an approach which enables the development of such models. Inspired by ideas and techniques from the distributional copula literature we investigate the procedure of nesting Archimedean Lévy copulas. We provide a detailed analysis of this construction, and derive conditions under which valid multivariate (nested) Lévy copulas are obtained. Our results are discussed and illustrated, notably with an example of model fitting to data.

Keywords: Lévy copula, Exchangeability, Dependence, Nested copulas, Insurance claims

JEL Classification: G22, C10

Suggested Citation

Avanzi, Benjamin and Tao, Jamie and Wong, Bernard and Yang, Xinda, Capturing Non-Exchangeable Dependence in Multivariate Loss Processes with Nested Archimedean Lévy Copulas (June 30, 2014). Forthcoming in Annals of Actuarial Science (2015) ; UNSW Australian School of Business Research Paper No. 2014ACTL05. Available at SSRN: https://ssrn.com/abstract=2461693 or http://dx.doi.org/10.2139/ssrn.2461693

Benjamin Avanzi

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

UNSW Sydney, NSW 2052
Australia

Jamie Tao

Westpac Bank ( email )

Sydney
Australia

UNSW Business School ( email )

UNSW Business School
High St
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

Xinda Yang

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

Sydney, NSW 2052
Australia

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