Convex ordering for random vectors using predictable representation

2008/01/30 by Arnaudon, Marc, Breton, Jean-Christophe, Privault, Nicolas
#60E15 #60G44 #60G55 #60H05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0801.4621

Abstract

We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends previous results in the one-dimensional case. We also study a geometric interpretation of convex ordering for discrete measures in connection with the conditions set on the jump heights and intensities of the considered processes.

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