Multidimensional Markovian BSDEs with Jumps and Continuous Generators

BSDEs with polynomial growth generators

In this paper, we give existence and uniqueness results for backward stochastic diierential equations when the generator has polynomial growth in the state variable. We deal with the case of xed terminal time as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic represen...

BSDEs with jumps in a general filtration

In this paper, we show existence and uniqueness of the solution of a multidimensional backward stochastic differential equation (BSDE). The aim is to extend several results on BSDE (L solutions, jumps, monotonicity, terminal random time, etc.) without assumption on the filtration. Introduction The notion of nonlinear backward stochastic differential equations (BSDEs for short) was introduced by...

Adding constraints to BSDEs with jumps: an alternative to multidimensional reflections

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 minimal solution for these so-called constrained BSDEs with jumps via a penalization procedure. This new type of BSDE offers a nice and practical unifying fram...

Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition

Quadratic BSDEs with convex generators and unbounded terminal conditions

In [3], the authors proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Unde...