This paper proves the existence and uniqueness of a solution to reflected backward stochastic differential equations with a lower obstacle, which is assumed to be right upper-semicontinuous. The result is established where the coefficient is stochastic Lipschitz by using some tools from the general theory of processes such as Mertens decomposition of optional strong supermartingales and other tools from optimal stopping theory.

This paper proves the existence and uniqueness of a solution to doubly reflected backward stochastic differential equations where the coefficient is stochastic Lipschitz, by means of the penalization method.

We consider a doubly reflected backward stochastic differential equations with jumps where the lower barrier and the opposite of the upper barrier are assumed to be right upper-semicontinuous (not necessarily càdlàg). We provide existence and uniqueness result when the coefficient is stochastic Lipschitz by using an equivalent transformation which is a coupled system of one-reflected backward stochastic differential equations.

No abstract

No abstract

No abstract

No abstract

In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson random measure. The existence and uniqueness of the solution is shown, firstly when the coefficients are stochastic Lipschitz, and secondly by weakening the conditions on the stochastic growth coefficient.