I. P. Van and . Berg, Principles of infinitesimal stochastic and financial analysis, World Scientific, 2000.

I. P. Van and . Berg, Discretisations of higher order and the theorems of Faà di Bruno and DeMoivre-Laplace, Journal of Logic and Analysis, vol.5, issue.6, 2013.

N. J. Cutland, P. E. Kopp, W. Willinger, and M. C. Wyman, Convergence of Snell Envelopes and Critical Prices in the American Put, Mathematics of Derivative Securities, 1997.

F. Diener and G. Reeb, Analyse Non Standard, 1995.

A. Friedman, Parabolic variational inequalities in one space dimension and smoothness of the free boundary, Journal of Functional Analysis, vol.18, issue.2, 1975.
DOI : 10.1016/0022-1236(75)90022-1

M. Gevrey, Sur les équations aux dérivées partielles du type parabolique, Journal de Math. Pures et Appl, vol.9, issue.6, 1913.

D. Lamberton, Critical Price for an American Option near Maturity, Seminar on stochastic analysis Birkhauser, Progress in Probability, 1995.
DOI : 10.1007/978-3-0348-7026-9_24

D. P. Leisen, Pricing the American put option: A detailed convergence analysis for binomial models, Journal of Economic Dynamics and Control, vol.22, issue.8-9, 1998.
DOI : 10.1016/S0165-1889(98)00019-0

P. L. Van-moerbeke, An optimal stopping problem with linear reward, Acta Mathematica, vol.132, issue.0, 1974.
DOI : 10.1007/BF02392110

P. L. Van-moerbeke, On optimal stopping and free boundary problems, Rational Mech. Anal, vol.60, 1976.

E. Nelson, Radically Elementary Probability Theory A discrete free boundary problem -235 ARIMA journal, 1987.
DOI : 10.1515/9781400882144