Optimal stopping via measure transformation: the Beibel–Lerche approach

Abstract

Optimal stopping of diffusions and related processes is usually done by solving a free boundary problem. In this paper, we propagate an alternative way, which has already been described in two earlier papers of Beibel and Lerche; we call it the B–L approach. It can be viewed as optimal stopping via measure transformation. While we emphasized in Beibel and Lerche a rather algebraic view, we describe here more the analytic side of the approach. Finally, it is related to some recent Jamshidian's results on a duality in optimal stopping.

Keywords:

• Optimal stopping
• The B–L approach
• Repeated significance test
• Disruption problem
• Russian option
• Lookback option

Acknowledgements

The authors are grateful to F. Jamshidian for helpful discussions and valuable suggestions and to anonymous referees whose comments helped to improve the paper.

Notes

^¶ [email protected]

^§This paper was written while the second author held a research fellowship of the Alexander von Humboldt-Stiftung.

Additional information

Notes on contributors

Mikhail Urusov

¶ ¶ [email protected] § §This paper was written while the second author held a research fellowship of the Alexander von Humboldt-Stiftung.