Measuring tail dependence for aggregate collateral losses using bivariate compound shot-noise Cox process

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 fre-quency 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 illustra-tions, a member of Farlie-Gumbel-Morgenstern copula with exponential margins is used. The figures of the joint distri-butions of collateral losses, their contours and numerical calculations of risk measures are also provided.