Abstract (EN)

We provide an obstacle version of the Geometric Dynamic ProgrammingPrinciple of Soner and Touzi (J. Eur. Math. Soc. 4:201–236, 2002) for stochastictarget problems. This opens the doors to a wide range of applications, particularly inrisk control in finance and insurance, in which a controlled stochastic process has tobe 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-hedging cost of American options under portfolio constraints, without appealing tothe standard dual formulation from mathematical finance. In particular, we allow fora degenerate volatility, a case which does not seem to have been studied so far in thiscontext.