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.

We show the existence of efficient hedge strategies for an investor facing the problem of a lack of initial capital for implementing a (super-) hedging strategy for an American contingent claim in a general incomplete market. In order to optimize we consider the maximization of the expected...