Mean-field doubly reflected backward stochastic differential equations

A New Type of Reflected Backward Doubly Stochastic Differential Equations

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 equations have been already studied by Ma and Wang [26]. They called it as ”variant” reflected BSDEs (VRBSDEs in short) based on the general version of the S...

Reflected backward doubly stochastic differential equations with time delayed generators

We consider a class of reflected backward doubly stochastic differential equations with time delayed generator (in short RBDSDE with time delayed generator), in this case generator at time t can depend on the values of a solution in the past. Under a Lipschitz condition, we ensure the existence and uniqueness of the solution.

Reflected Solutions of Backward Doubly Stochastic Differential Equations ∗

We study reflected solutions of one-dimensional backward doubly stochastic differential equations (BDSDEs in short). The “reflected” keeps the solution above a given stochastic process. We get the uniqueness and existence by penalization. For the existence of backward stochastic integral, our proof is different from [KKPPQ] slightly. We also obtain a comparison theorem for reflected BDSDEs. At ...

Mean Field Forward-Backward Stochastic Differential Equations

The purpose of this note is to provide an existence result for the solution of fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of the mean field type. These equations occur in the study of mean field games and the optimal control of dynamics of the McKean Vlasov type.

On Solving Backward Doubly Stochastic Differential Equations