Supermodular ordering of Poisson arrays

Bünyamin Kızıldemir and Nicolas Privault

Statistics & Probability Letters, 2015, vol. 98, issue C, 136-143

Abstract: 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.

Keywords: Stochastic ordering; Supermodular functions; Infinitely divisible random vectors; Poisson distribution; Jump–diffusion models (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2014.12.021

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