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Journal of Function Spaces
Volume 2015 (2015), Article ID 245436, 5 pages
http://dx.doi.org/10.1155/2015/245436
Research Article

The Randomized American Option as a Classical Solution to the Penalized Problem

American University of Sharjah, P.O. Box 26666, Sharjah, UAE

Received 13 August 2015; Accepted 7 October 2015

Academic Editor: Hugo Leiva

Copyright © 2015 Guillaume Leduc. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We connect the exercisability randomized American option to the penalty method by showing that the randomized American option value is the unique classical solution to the Cauchy problem corresponding to the canonical penalty problem for American options. We also establish a uniform bound for , where is the infinitesimal generator of a geometric Brownian motion.