Geodesic
The American Put Option Close to Expiry
Acta mathematica Universitatis Comenianae, Tome 73 (2004) no. 2 
R. Mallier; G. Alobaidi. The American Put Option Close to Expiry. Acta mathematica Universitatis Comenianae, Tome 73 (2004) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2004_73_2_a3/
@article{AMUC_2004_73_2_a3,
     author = {R. Mallier and G. Alobaidi},
     title = {The {American} {Put} {Option} {Close} to {Expiry}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2004},
     volume = {73},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2004_73_2_a3/}
}
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Voir la notice de l'article provenant de la source Comenius University

We use an asymptotic expansion to study the behavior of the American put option close to expiry for the case where the dividend yield is less than or equal to the risk-free interest rate. Series solutions are obtained for the location of the free boundary and the price of the option in that limit.