FBSDE with time delayed generators: Lp-solutions, differentiability, representation formulas and path regularity

Original · EN

We extend the work of Delong and Imkeller (2010a,b) concerning Backward stochastic differential equations with time delayed generators (delay BSDE). We give moment and a priori estimates in general Lᵖ-spaces and provide sufficient conditions for the solution of a delay BSDE to exist in Lᵖ. We introduce decoupled systems of SDE and delay BSDE (delay FBSDE) and give sufficient conditions for their variational differentiability. We connect these variational derivatives to the Malliavin derivatives of delay FBSDE via the usual representation formulas. We conclude with several path regularity results, in particular we extend the classic L²-path regularity to delay FBSDE.