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We derive necessary and sufficient conditions for the supermodular ordering of certain triangular arrays of Poisson random variables, based on the componentwise ordering of their covariance matrices. Applications are proposed for markets driven by jump–diffusion processes, using sums of Gaussian and Poisson random vectors. Our results rely on a new triangular structure for the representation of Poisson random vectors using their Lévy–Khintchine representation. [ABSTRACT FROM AUTHOR]

Abstract: Using finite difference operators, we define a notion of boundary and surface measure for configuration sets under Poisson measures. A Margulis–Russo type identity and a co-area formula are stated with applications to bounds on the probabilities of monotone sets of configurations and on related isoperimetric constants. [Copyright &y& Elsevier]