On the put-call duality of the game options

The purpose of this paper is to obtain a duality between the game put and call options assuming three component penalties – proportion of the usual option payoff, shares of the underlying asset, and a fixed amount. We examine separately the cases of finite and infinite maturities. For the perpetual options, we need to derive a polynomial-style equations for the optimal boundaries. We prove the existence and uniqueness of their solutions as well as provide a method for their deriving. This result