Adrien Richou

On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions

In a previous work, P. Briand and Y. Hu proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved by P. Briand and Y. Hu.

Numerical simulation of BSDEs with drivers of quadratic growth

This article deals with the numerical resolution of Markovian backward stochastic differential equations (BSDEs) with drivers of quadratic growth with respect to

Numerical simulation of quadratic BSDEs

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Ergodic BSDEs and related PDEs with Neumann boundary conditions

and bounded terminal conditions. We first show some bound estimates on the process

A Probabilistic Approach to Large Time Behavior of Mild Solutions of HJB Equations in Infinite Dimension

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Large deviations for the Ornstein-Uhlenbeck process with shift

and we specify the Zhangs path regularity theorem. Then we give a new time discretization scheme with a non uniform time net for such BSDEs and we obtain an explicit convergence rate for this scheme.

Numerical Stability Analysis of the Euler Scheme for BSDEs

This article deals with the numerical approximation of Markovian backward stochastic differential equations (BSDEs) with generators of quadratic growth with respect to

A note on the existence of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition

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Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition

and bounded terminal conditions. We first study a slight modification of the classical dynamic programming equation arising from the time-discretization of BSDEs. By using a linearization argument and BMO martingales tools, we obtain a comparison theorem, a priori estimates and stability results for the solution of this scheme. Then we provide a control on the time-discretization error of order

On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: The critical case

\frac{1}{2}-\varepsilon