Before revision: In this paper we study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in the  Heath-Jarrow-Morton (HJM) framework for the forward interest rate. In particular we consider its Musiela's parametrization to guarantee a Markovian setting. Hence we are in an infinite dimensional setting, in which the forward rate curve is described by a SDE in a suitable Hilbert space. 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.
After revision: In this paper we study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in the Heath-Jarrow-Morton (HJM) model for forward interest rates. First we show regularity properties of the price function by probabilistic methods. Then we 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.