The American version of the Geometric Dynamic Programming Principle : Application to the pricing of American options under constraints

We provide an American version of the Geometric Dynamic Programming Principle of Soner and Touzi [22] for stochastic target problems. This opens the doors to a wide range of applications, particularly in risk control in finance and insurance, in which a controlled stochastic process has to be maintained in a given set on a time interval [0, T ]. As an example of application, we show how it can be used to provide a viscosity characterization of the super-heging price of American options under portfolio constraints, without appealing to the standard dual formulation from mathematical finance. In particular, we allow for a degenerate volatility, a case which does not seem to have been studied so far in this context.