High Dimensional Modelling and Simulation with Asymmetric Normal Mixtures

18 Pages Posted: 11 Aug 2007

See all articles by Andreas Tsanakas

Andreas Tsanakas

Bayes Business School (formerly Cass), City, University of London

Andrew D. Smith

University College Dublin (UCD); Deloitte Touche Tohmatsu

Date Written: July 20, 2007

Abstract

A family of multivariate distributions, based on asymmetric normal mixtures, is introduced in order to model the dependence among insurance and financial risks. The model allows for straight-forward parameterisation via a correlation matrix and enables the modelling of radially asymmetric dependence structures, which are often of interest in risk management applications. Dependence is characterised by showing that increases in correlation values produce models which are ordered in the supermodular order sense. Explicit expressions for the Spearman and Kendall rank correlation coefficients are derived to enable calibration in a copula framework. The model is adapted to simulation in very high dimensions by using Kronecker products, enabling specification of a correlation matrix and an increase in computational speed.

Keywords: Dependence, copula, normal mixtures, Kronecker product,

Suggested Citation

Tsanakas, Andreas and Smith, Andrew D., High Dimensional Modelling and Simulation with Asymmetric Normal Mixtures (July 20, 2007). Available at SSRN: https://ssrn.com/abstract=1005894 or http://dx.doi.org/10.2139/ssrn.1005894

Andreas Tsanakas (Contact Author)

Bayes Business School (formerly Cass), City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Andrew D. Smith

University College Dublin (UCD) ( email )

Belfield
Belfield, Dublin 4 4
Ireland

Deloitte Touche Tohmatsu ( email )

Paramount Plaza
Midtown Manhattan
New York, NY AB
United States

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