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Free boundary and American options in a jump-diffusion model

The purpose of this paper is to give a pricing analysis for the American option in a jump-diffusion model by PDE arguments. Existence and uniqueness of the solution to the obstacle problem for the associated model is shown in suitable spaces. We also prove the unique existence of the solution of the corresponding free boundary problem. Furthermore, smoothness and monotonicity of the free boundary which is the optimal exercise boundary of the option are deduced.