Convex hedging of non-superreplicable claims in discrete-time market models

All of the papers written so far deal with efficient hedging of contingent claims for which superhedging exists. The goal of this paper is to investigate the convex hedging of contingent claims for which superhedging does not exist. Without superhedging assumption it is still possible to prove the existence of a solution, but one cannot obtain structure of the solution using techniques known so far. Therefore, we develop a new approximative approach to deduce structure of the solution in case of non-superreplicable claims.