We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims.

A coupled forward–backward stochastic differential system (FBSDS) is formulated in spaces of fields for the incompressible Navier–Stokes equation in the whole space. It is shown to have a unique local solution, and further if either the Reynolds number is small or the dimension of the...

A local strict comparison theorem and some converse comparison theorems are proved for reflected backward stochastic differential equations under suitable conditions.

We prove an existence and uniqueness theorem for backward stochastic differential equations driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one.

A market is described by two correlated asset prices. But only one of them is traded while the contingent claim is a function of both assets. We solve the mean-variance hedging prob- lem completely and prove that the optimal strategy consists of a modified pure hedge expressible in terms of the...