Measuring Tail Dependence for Aggregate Collateral Losses Using Bivariate Compound Shot-Noise Cox Process

Jiwook Jang, Genyuan Fu

Benelec Pty Ltd., Sydney, Australia.
Department of Applied Finance & Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, Australia.

DOI: 10.4236/am.2012.312A300                

Abstract

In this paper, we introduce tail dependene measures for collateral losses from catastrophic events. To calculate these measures, we use bivariate compound process where a Cox process with shot noise intensity is used to count collateral losses. A homogeneous Poisson process is also examined as its counterpart for the case where the catastrophic loss frequency rate is deterministic. Joint Laplace transform of the distribution of the aggregate collateral losses is derived and joint Fast Fourier transform is used to obtain the joint distributions of aggregate collateral losses. For numerical illustrations, a member of Farlie-Gumbel-Morgenstern copula with exponential margins is used. The figures of the joint distributions of collateral losses, their contours and numerical calculations of risk measures are also provided.

Keywords

Aggregate Collateral Losses; Bivariate Compound Cox Process; Shot Noise Process; Farlie-Gumbel-Morgenstern Copula; Tail Dependence; Joint Fast Fourier Transform

Conflicts of Interest

The authors declare no conflicts of interest.

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