International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 264603, 28 pages
Research Article

Optimal Selling Rule in a Regime Switching Lévy Market

Department of Mathematics, Towson University, Towson, MD 21252-0001, USA

Received 5 March 2011; Accepted 5 April 2011

Academic Editor: Giuseppe Marino

Copyright © 2011 Moustapha Pemy. 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.


This paper is concerned with a finite-horizon optimal selling rule problem when the underlying stock price movements are modeled by a Markov switching Lévy process. Assuming that the transaction fee of the selling operation is a function of the underlying stock price, the optimal selling rule can be obtained by solving an optimal stopping problem. The corresponding value function is shown to be the unique viscosity solution to the associated HJB variational inequalities. A numerical example is presented to illustrate the results.