Related papers: Discrete-time approximation of multidimensional BS…

We are concerned with high-dimensional coupled FBSDE systems approximated by the deep BSDE method of Han et al. (2018). It was shown by Han and Long (2020) that the errors induced by the deep BSDE method admit a posteriori estimate…

We introduce and study a new class of optimal switching problems, namely switching problem with controlled randomisation, where some extra-randomness impacts the choice of switching modes and associated costs. We show that the optimal value…

This paper studies a system of multi-dimensional reflected backward stochastic differential equations with oblique reflections (RBSDEs for short) in infinite horizon associated to switching problems. The existence and uniqueness of the…

Backward stochastic differential equations (BSDEs) appear in numeruous applications. Classical approximation methods suffer from the curse of dimensionality and deep learning-based approximation methods are not known to converge to the BSDE…

We establish upper bounds for the $L^p$-quantization error, p in (1, 2+d), induced by the recursive Markovian quantization of a d-dimensional diffusion discretized via the Euler scheme. We introduce a hybrid recursive quantization scheme,…

Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distances for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long…

This article deals with the numerical resolution of Markovian backward stochastic differential equations (BSDEs) with drivers of quadratic growth with respect to $z$ and bounded terminal conditions. We first show some bound estimates on the…

This paper is devoted to the study of reflected Stochastic Differential Equations when the constraint is not on the paths of the solution but acts on the law of the solution. These reflected equations have been introduced recently by…

This paper shows that penalized backward stochastic differential equation (BSDE), which is often used to approximate and solve the corresponding reflected BSDE, admits both optimal stopping representation and optimal control representation.…

We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the Feynman-Kac representation in [12] by means of control…

The paper is directly motivated by the pricing of vulnerable European and American options in a general hazard process setup and a related study of the corresponding pre-default backward stochastic differential equations (BSDE) and…

We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove existence and uniqueness results. We also show that the…

The present paper is devoted to the study of backward stochastic differential equations with mean reflection formulated by Briand et al. [7]. We investigate the solvability of a generalized mean reflected BSDE, whose driver also depends on…

We study the approximation of backward stochastic differential equations (BSDEs for short) with a constraint on the gains process. We first discretize the constraint by applying a so-called facelift operator at times of a grid. We show that…

We study the quantitative stability of the solutions to Markovian quadratic reflected BSDEs with bounded terminal data. By virtue of BMO martingale and change of measure techniques, we obtain stability estimates for the variation of the…

In this paper, we study the backward stochastic differential equation (BSDE) with two nonlinear mean reflections, which means that the constraints are imposed on the distribution of the solution but not on its paths. Based on the backward…

This paper is devoted to the study of reflected Stochastic Differential Equations with jumps when the constraint is not on the paths of the solution but acts on the law of the solution. This type of reflected equations have been introduced…

We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of…

We investigate the convergence rate for the time discretization of a class of quadratic backward SDEs -- potentially involving path-dependent terminal values -- when coupled with non-standard Lipschitz-type forward SDEs. In our review of…

The present paper is devoted to the study of the well-posedness of BSDEs with mean reflection whenever the generator has quadratic growth in the $z$ argument. This work is the sequel of Briand et al. [BSDEs with mean reflection,…