Measuring tail dependence for collateral losses using bivariate Lévy process

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Jiwook Jang, Australia
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Summary:
In practice, insurance companies face collateral losses, for example, in worldwide, once a storm or earthquake arrives, it brings about damages in properties, motors and interruption of businesses. It occurred a couple of losses simultaneously from the World Trade Centre (WTC) catastrophe. However it has not been developed an applicable model for insurance companies to measure stochastic dependence for these ollateral losses. The aim of this paper is to measure (upper) tail dependence for collateral losses, employing ivariate Lévy process, i.e. bivariate compound Poisson process with a copula, as insurance industry is more concerned with dependence between extreme values. In order to derive an explicit expression of joint Laplace transform of collateral losses, we use a member of Farlie-Gumbel-Morgenstern copula with exponential margins. Inversion of joint Fast Fourier transform obtained from the joint Laplace transform of collateral losses is used to calculate the coefficients of (upper) tail dependence numerically. We also provide the figures of the joint distribution of collateral losses and their contours at each value of the parameter in a Farlie-Gumbel-Morgenstern copula.
 
Date: 30 May - Time: 8:30 to 10:00 - Room: 251
Theme: 1.A. Stochastic dependence