Related papers: Mean reflected BSDE driven by a marked point proce…

In this work, we develop the discrete solvability analysis for perturbed saddle-point problems in Banach spaces with forcing terms regularised by means of a projector constructed using the adjoint of a weighted Cl\'ement…

We consider several critical wetting models. In the discrete case, these probability laws are known to converge, after an appropriate rescaling, to the law of a reflecting Brownian motion, or of the modulus of a Brownian bridge, according…

We consider reflected generalized backward doubly stochastic differential equations driven by a non-homogeneous L\'evy process. Under stochastic conditions on the coefficients, we prove the existence and uniqueness of a solution.…

This article constructs a forward exponential utility in a market with multiple defaultable risks. Using the Jacod-Pham decomposition for random fields, we first characterize forward performance processes in a defaultable market under the…

We prove results on bounded solutions to backward stochastic equations driven by random measures. Those bounded BSDE solutions are then applied to solve different stochastic optimization problems with exponential utility in models where the…

We consider dynamic risk measures induced by Backward Stochastic Differential Equations (BSDEs) in enlargement of filtration setting. On a fixed probability space, we are given a standard Brownian motion and a pair of random variables…

We consider ergodic backward stochastic differential equations, in a setting where noise is generated by a countable state uniformly ergodic Markov chain. We show that for Lipschitz drivers such that a comparison theorem holds, these…

In this paper we provide conditions for the existence of supersolutions to BSDEs with mean-reflections on the $Z$ component. We show that, contrary to BSDEs with mean-reflections on the $Y$ component, we cannot expect a supersolution with a…

In this paper, an optimal switching problem is proposed for one-dimensional reflected backward stochastic differential equations (RBSDEs, for short) where the generators, the terminal values and the barriers are all switched with positive…

Motivated by liquidity risk in mathematical finance, D. Lacker introduced concentration inequalities for risk measures, i.e. upper bounds on the \emph{liquidity risk profile} of a financial loss. We derive these inequalities in the case of…

This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDDSEs) in a convex domain D. Moreover, using a stochastic flow approach a probabilistic interpretation for a…

This paper mainly investigates reflected stochastic recursive control problems governed by jump-diffusion dynamics. The system's state evolution is described by a stochastic differential equation driven by both Brownian motion and Poisson…

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…

In this paper, we prove new convergence results improving the ones by Chassagneux, Elie and Kharroubi [Ann. Appl. Probab. 22 (2012) 971--1007] for the discrete-time approximation of multidimensional obliquely reflected BSDEs. These BSDEs,…

In this paper, we study the solvability of a class of multi-dimensional forward backward stochastic differential equations (FBSDEs) with oblique reflection and unbounded stopping time. Under some mild assumptions on the coefficients in such…

We study a discrete time approximation scheme for the solution of a doubly reflected Backward Stochastic Differential Equation (DBBSDE in short) with jumps, driven by a Brownian motion and an independent compensated Poisson process.…

In the first part of this paper, we study RBSDEs in the case where the filtration is not quasi-left continuous and the lower obstacle is given by a predictable process. We prove the existence and uniqueness by using some results of optimal…

In this paper, we introduce a new kind of "variant" reflected backward doubly stochastic differential equations (VRBDSDEs in short), where the drift is the nonlinear function of the barrier process. In the one stochastic case, this type of…

This paper studies Merton's problem in an extended formulation by incorporating the benchmark tracking on the wealth process. We consider a tracking formulation where the fund manager aims to maximize the trade-off between the expected…

This paper establishes the well-posedness of reflected backward stochastic differential equations in the non-convex domains that satisfy a weaker version of the star-shaped property. The main results are established (i) in a Markovian…