Non-Markovian Fully Coupled Forward-Backward Stochastic Systems and   Classical Solutions of Path-dependent PDEs
  This paper explores the relationship between non-Markovian fully coupled forward-backward stochastic systems and path-dependent PDEs. The definition of classical solution for the path-dependent PDE is given within the framework of functional It\^{o} calculus. Under mild hypotheses, we prove that the forward-backward stochastic system provides the unique classical solution to the path-dependent PDE. 
Shaolin Ji, Shuzhen Yang
math.PR math.AP