There are many web sites that contain notes for courses on
stochastic calculus or finance. See, for example, Per Myklund's pages
for two courses, Stat 390 and
Stat 391. The former has a link through to some nice lecture notes
by Steve Lalley.
Per recommended to me several papers, which are are mentioned on the
Stat 391 page:

The paper by Miyani talks about American options, but it gets into
heavy math pretty quickly.
 The paper by Longstaff and Schwartz describes a method for
approximating the value of American options.

Foellmer and Leukert
 Volume 21 issues 89 of Journal of Economic Dynamics and
Control , in particular the paper by Phelim Boyle, Mark Broadie
and Paul Glasserman. You can obtain this paper online, starting
from the link to Online Journals and Newspapers on the Research Tools
page at the Yale Library.
I have not yet looked at these papers in any detail.