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We prove results relating to the exit time of a stochastic process from a region in N-dimensional space. We compute certain stochastic integrals involving the exit time. Taking a Gaussian copula model for the hitting time behavior, We derive explicit formulas for CDO tranche sensitivity to parameter variations, and prove results concerning the qualitative behavior of such tranche sensitivities, as well as the large-N behavior, for a homogeneous portfolio governed by the one-factor Gaussian copula. A Poisson-mixture model is also investigated in a similar vein. Relevant simulations are presented.

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Chao Meng expects his M.Eng. in Financial Engineering in Dec. 2009 in Cornell University. He also holds a Ph.D. in mathematics from Louisiana State University (LSU) and bachelor s degree in mathematics from University of Sci. & Tech. of China (USTC). His research has been focused on stochastic analysis with applications in finance.

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