Markovian forward–backward stochastic differential equations and stochastic flows

Markovian forward–backward stochastic differential equations, (MFBSDEs), are discussed by exploiting techniques of stochastic flows. Using martingale representation, a differentiation rule, stochastic flows of diffeomorphisms and the unique decomposition of special semimartingales, we identify the solution of the backward system of the FBSDE. Applications of the result to convex risk measures are discussed.