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 capital is insufficient for a perfect hedge. This problem has been solved under complete information on the underlying model in [3].  We present two...

The paper deals with a class of semi-Markov control models with Borel state and control spaces, possibly unbounded costs, and unknown holding times distribution H. Assuming that H does not depend on state-action pairs, we combine suitable methods of statistical estimation of H with control...