Calcul de Malliavin et probabilité invariante d'une chaîne de Markov
Calcul de Malliavin et régularité de la densité d'une probabilité invariante d'une chaîne de Markov
Calcul stochastique non adapté par rapport à la mesure aléatoire de Poisson
Central and non-central limit theorems for weighted power variations of fractional brownian motion
In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q≥2 of the fractional brownian motion with Hurst parameter H∈(0, 1), where q is an integer. The central limit holds for 1/2q<H≤1−1/2q, the limit being a conditionally gaussian distribution. If H<1/2q we show the convergence in L2 to a limit which only depends on the fractional brownian motion, and if H>1−1/2q we show the convergence in L2 to a stochastic integral...
Clark–Ocone formulas and Poincaré inequalities on the discrete cube
Classical and variational differentiability of BSDEs with quadratic growth.
Comparison principle approach to utility maximization
We consider the problem of optimal investment for maximal expected utility in an incomplete market with trading strategies subject to closed constraints. Under the assumption that the underlying utility function has constant sign, we employ the comparison principle for BSDEs to construct a family of supermartingales leading to a necessary and sufficient condition for optimality. As a consequence, the value function is characterized as the initial value of a BSDE with Lipschitz growth.
Computation of Greeks for barrier and look-back options using Malliavin calculus.
Computation of Greeks using Malliavin's calculus in jump type market models.
Construction de l'opérateur de Malliavin sur l'espace de Poisson
Convergence in Dirichlet law of certain stochastic integrals.
Convex concentration inequalities and forward-backward stochastic calculus.