Some optimal stopping problems for pricing game options

A game option is a general American-type option with the added possibility that not only the option holder, but also the option writer, may terminate the contract at any time. In this paper, We establish some equivalent forms between game option pricing problems and reflected backward stochastic differential equations (RBSDEs for short) with one reflected barrier and obtain the existence and uniqueness of the solution for the game option. By applying the RBSDE methods, we obtain some properties of value function of the game option and prove the comparison theorem for RBSDEs with one reflected barrier.