<t>Zhu from the University of Wollongong (Australia) has a closed form solution for the american put. See Noise and Fluctuations in Econophysics and Finance. Edited by Abbott, Derek; Bouchaud, Jean-Philippe; Gabaix, Xavier; McCauley, Joseph L. Proceedings of the SPIE, Volume 5848, pp. 186-199 (2005)...