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In this paper, we deal with the valuation of Game Russian option with jumps, which is a contract that the seller and the buyer have both the rights to cancel and to exercise it at any time, respectively. This model can be formulated as a coupled optimal stopping problem. First, we discuss the pricing model with jumps when the stock pays dividends continuously. Secondly, we derive the value function of Game Russian options and investigate properties of optimal boundaries of the buyer. Finally, some numerical results are presented to demonstrate analytical properties of the value function.

Game Russian Options for Double Exponential Jump Diffusion Processes