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Your search keyword '"Privault, Nicolas"' showing total 4 results
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4 results on '"Privault, Nicolas"'

1. Convex ordering for random vectors using predictable representation

Author

Arnaudon, Marc, Breton, Jean-Christophe, and Privault, Nicolas

Subjects
Mathematics - Probability, 60E15, 60H05, 60G44, 60G55
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.

Published
2008

3. Supermodular ordering of Poisson arrays.

Author

Kızıldemir, Bünyamin and Privault, Nicolas

Subjects
*POISSON processes, *TRIANGULARIZATION (Mathematics), *RANDOM variables, *COVARIANCE matrices, *VECTOR analysis, *STOCHASTIC orders
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. [ABSTRACT FROM AUTHOR]

Published
2015
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4. Convex comparison inequalities for non-Markovian stochastic integrals.

Author

Breton, Jean-Christophe, Laquerrière, Benjamin, and Privault, Nicolas

Subjects
CONVEX functions, COMPARATIVE studies, MATHEMATICAL inequalities, MARKOV processes, STOCHASTIC integrals, BROWNIAN motion, DIFFUSION processes
Abstract

We derive convex comparison inequalities for stochastic integrals of the formand, whereare adapted processes with respect to the filtration generated by a standard Brownian motion, andis an independent Brownian motion. Our method uses forward–backward stochastic integration and the Malliavin calculus, and is also applied to jump–diffusion processes. [ABSTRACT FROM AUTHOR]

Published
2013
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