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.
Deformation quantization in white noise analysis.
Delay equations driven by rough paths.
Density estimates on a parabolic SPDE.
Density formula and concentration inequalities with Malliavin calculus.
Dérivation stochastique de diffusions réfléchies
Développement asymptotique de la densité d'une diffusion dégénérée.
Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale
On obtient ici le développement asymptotique, en temps petit et sur la diagonale, du noyau de la chaleur associé à un opérateur dégénéré du second ordre satisfaisant à la condition forte d’hypoellipticité de Hörmander.
Differential equations driven by fractional Brownian motion.
A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.
Differential properties of measures on infinite dimensional spaces and the Malliavin calculus
Ergodicity of hypoelliptic SDEs driven by fractional brownian motion
We demonstrate that stochastic differential equations (SDEs) driven by fractional brownian motion with Hurst parameter H>½ have similar ergodic properties as SDEs driven by standard brownian motion. The focus in this article is on hypoelliptic systems satisfying Hörmander’s condition. We show that such systems enjoy a suitable version of the strong Feller property and we conclude that under a standard controllability condition they admit a unique stationary solution that is physical in the...
Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion.
Existence of density for the solution to the three-dimensional wave equation.
We prove existence of density for the real-valued solution to a 3-dimensional stochastic wave equation (...).
Forme de Dirichlet sur l'espace canonique de Poisson et applications aux équations différentielles stochastiques