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3 results on '"Privault, Nicolas"'

1. Convex concentration for some additive functionals of jump stochastic differential equations.

Author

Ma, Yutao and Privault, Nicolas

Subjects
*CONVEX geometry, *FUNCTIONALS, *STOCHASTIC differential equations, *MATHEMATICAL inequalities, *DERIVATIVES (Mathematics), *MATHEMATICAL bounds, *PROBABILITY theory
Abstract

Using forward-backward stochastic calculus, we prove convex concentration inequalities for some additive functionals of the solution of stochastic differential equations with jumps admitting an invariant probability measure. As a consequence, transportation-information inequalities are obtained and bounds on option prices for interest rate derivatives are given as an application. [ABSTRACT FROM AUTHOR]

Published
2013
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2. 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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3. 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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