Shortfall risk minimization under model uncertainty in the binomial case: adaptive and robust approaches

We consider the problem of minimizing the shortfall risk when the aim is to hedge a contingent claim in a binomial market model and the initial capita l is insufficient for a perfect hedge. This problem has been solved under c omplete information on the underlying model in [3]. We present two possible solutions to the same problem in the case of incomp lete information, namely when the underlying probability measure is unknown . The results obtained can also be applied to other classical problems, suc h as VaR minimization or maximum loss minimization.