2010/08/06 by Gonçalo dos Reis, Reis, Gonçalo dos, Anthony Réveillac +3
Economics, Econometrics and Finance · Engineering · Mathematics · #60G17 #60H07 #60H10 (Primary) #60H30 (Secondary) #FOS: Mathematics #Financial Risk and Volatility Modeling #Fluid Dynamics and Turbulent Flows #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60G17 #msc:60H07 #msc:60H10 #msc:60H30
paper · pdf · doi:10.48550/arxiv.1008.1149
Accepted for publication in Stochastic Processes and their Applications
openalex publication_date 2010/08/06 · arxiv created 2011/05/04 · arxiv updated 2011/05/05 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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.