This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Dayanik, S. Search for Related Content

Optimal Stopping of Linear Diffusions with Random Discounting

Department of Operations Research and Financial Engineering and the Bendheim Center for Finance, Princeton University, Princeton, New Jersey 08544
sdayanik{at}princeton.edu, http://www.princeton.edu/sdayanik

We propose a new solution method for optimal stopping problems with random discounting for linear diffusions whose state space has a combination of natural, absorbing, or reflecting boundaries. The method uses a concave characterization of excessive functions for linear diffusions killed at a rate determined by a Markov additive functional and reduces the original problem to an undiscounted optimal stopping problem for a standard Brownian motion. The latter can be solved essentially by inspection. The necessary and sufficient conditions for the existence of an optimal stopping rule are proved when the reward function is continuous. The results are illustrated on examples.

Key Words: optimal stopping; diffusions; additive continuous functionals; excessive functions; concavity; smooth-fit principle
History: Received: April 3, 2007; revision received: November 22, 2007;