Before revision:  In order to find an infinite dimensional variational formulation of the pricing problem , we extend some results on infinite dimensional optimal stopping and variational inequalities recently obtained in 8 . The proof goes through three main steps. First we regularize the American bond option's payoff by adopting usual smoothing arguments. Next we approximate the infinite dimensional dynamics by finite dimensional ones to which we associate suitable optimal stopping problems in R^n.
After revision:  In order to find an infinite dimensional variational formulation of the pricing problem , we extend some results on infinite dimensional optimal stopping and variational inequalities recently obtained in 8 by approximating the original optimal stopping problem by finite dimensional ones to which we associate suitable optimal stopping problems in R^n.