(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity. In this paper, we consider the problem of hedging Game Contingent Claims (GCC) in two cases. For the case that portfolio is unconstrained, we provide a single arbitrage-free price P_0. Whereas for the constrained case, the price is replaced by an interval [h_low,h_up] of arbitrage-free prices. And for the portfolio with some closed constraints, we give the expressions of the upper-hedging price and lower-hedging price. Finally, for a special type of game option, we provide explicit expressions of the price and optimal portfolio for the writer and holder.