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Stochastic control and applications to finance
This thesis contains three parts that can be read independently. In the first part, we study the resolution of stochastic control problems by quantization methods. The... -
Stochastic representation for solutions of Isaacs' type integral-partial diff...
International audience -
GKW representation theorem and linear BSDEs under restricted information. An ...
International audience -
Quadratic Backward Stochastic Differential Equations (BSDEs) Driven by a Cont...
International audience -
Density estimates for solutions to one dimensional Backward SDE's
International audience -
A Parallel Algorithm for solving BSDEs
International audience -
Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps
We study the optimal stopping problem for dynamic risk measures represented by Backward Stochastic Differential Equations (BSDEs) with jumps and its relation with... -
BSDEs under partial information and financial applications.
In this paper we provide existence and uniqueness results for the solution of BSDEs driven by a general square integrable martingale under partial information. We... -
Stochastic methods in molecular dynamic
This thesis presents two independent research topics. Both are related to the application of stochastic problems to molecular dynamics. In the first part, we present a... -
Dual and backward SDE representation for optimal control of non-Markovian SDEs
We study optimal stochastic control problem for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients, and gain functionals... -
Some applications of BSDE theory: fractional BDSDEs and regularity properties...
In the first part of my thesis, by adapting the idea of Jien and Ma (2010), the main objective is to study the (semilinear or linear) doubly stochastic differential... -
A numerical algorithm for fully nonlinear HJB equations: an approach by contr...
We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9]... -
Discrete time approximation of fully nonlinear HJB equations via BSDEs with n...
We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is... -
Switching Game of Backward Stochastic Differential Equations and Associated S...
This paper is concerned with the switching game of a one-dimensional backward stochastic differential equation (BSDE). The associated Bellman-Isaacs equation is a... -
BSDEs with weak terminal condition
We introduce a new class of Backward Stochastic Differential Equations in which the $T$-terminal value $Y_{T}$ of the solution $(Y,Z)$ is not fixed as a random... -
Approximation of backward stochastic differential equations using Malliavin w...
We design a numerical scheme for solving a Dynamic Programming equation with Malliavin weights arising from the time-discretization of backward stochastic differential...
