Related papers: Strong envelope and strong supermartingale: applic…

The present paper is devoted to the study of the well-posedness of mean field BSDEs with mean reflection and nonlinear resistance. By the contraction mapping argument, we first prove that the mean-field BSDE with mean reflection and…

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…

We consider a robust impulse control problem in finite horizon where the underlying uncertainty stems from an impulsively and continuously controlled functional stochastic differential equation (FSDE) driven by Brownian motion. We assume…

Robust Markov decision processes (MDPs) have attracted significant interest due to their ability to protect MDPs from poor out-of-sample performance in the presence of ambiguity. In contrast to classical MDPs, which account for…

Robustness is important for sequential decision making in a stochastic dynamic environment with uncertain probabilistic parameters. We address the problem of using robust MDPs (RMDPs) to compute policies with provable worst-case guarantees…

We study penalization coupled with time discretization for decoupled Markovian doubly reflected BSDEs with obstacles \(p_b(t,X_t)\le Y_t\le p_w(t,X_t)\). The DRBSDE is approximated by a penalized BSDE with parameter \(\lambda\) and…

We compare numerically the performance of reversible and non-reversible Markov Chain Monte Carlo algorithms for high dimensional oil reservoir problems; because of the nature of the problem at hand, the target measures from which we sample…

We consider BSDEs with two reflecting irregular barriers. We give necessary and sufficient conditions for existence and uniqueness of $\mathbb{L}^{p}$ solutions for equations with generators monotone with respect to $y$ and Lipschitz…

This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a…

In this paper, we introduce a new method to study the doubly reflected backward stochastic differential equation driven by G-Brownian motion (G-BSDE). Our approach involves approximating the solution through a family of penalized reflected…

In this paper, we prove the existence and uniqueness result of the reflected BSDE with two continuous barriers under monotonicity and general increasing condition on $y$, with Lipschitz condition on $z$.

We solve the optimal control problem of a one-dimensional reflected stochastic differential equation, whose coefficients can be path dependent. The value function of this problem is characterized by a backward stochastic partial…

We solve a class of doubly reflected backward stochastic differential equation whose generator depends on the resistance due to reflections, which extend the recent work of Qian and Xu on reflected BSDE with one barrier. We then obtain the…

We prove that under natural assumptions on the data strong solutions in Sobolev spaces of semilinear parabolic equations in divergence form involving measure on the right-hand side may be represented by solutions of some generalized…

We propose \textit{DeepMartingale}, a deep-learning framework for the dual formulation of discrete-monitoring optimal stopping problems under continuous-time models. Leveraging a martingale representation, our method implements a…

Fueled by advances in both robust optimization theory and reinforcement learning (RL), robust Markov Decision Processes (RMDPs) have garnered increasing attention due to their powerful capability for sequential decision-making under…

In this paper, we propose a new notion of Forward--Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the forward--backward stochastic differential equations (FBSDEs). The FBMP extends the idea of the…

Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…

In this paper, we study the doubly reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs for short) when the generator has quadratic growth in the $z$-component. Based on the theory of $G$-BMO…

Robust Markov Decision Processes (MDPs) are receiving much attention in learning a robust policy which is less sensitive to environment changes. There are an increasing number of works analyzing sample-efficiency of robust MDPs. However,…