  We study partial hedging for game options in markets with transaction costs
bounded from below. More precisely, we assume that the investor's transaction
costs for each trade are the maximum between proportional transaction costs and
a fixed transaction costs. We prove that in the continuous time Black--Scholes
(BS) model, there exists a trading strategy which minimizes the shortfall risk.
Furthermore, we use binomial models in order to provide numerical schemes for
the calculation of the shortfall risk and the corresponding optimal portfolio
in the BS model.
