Examples of optimal stopping via measure transformation for processes with one-sided jumps

Abstract

In this short note, we show that the method introduced by Beibel and Lerche (1997) for solving certain optimal stopping problems for Brownian motion can be applied as well to some optimal stopping problems involving processes with one-sided jumps.

Keywords:

• Optimal stopping problems
• Spectrally negative Lévy processes
• Stable processses
• Generalised Ornstein–Uhlenbeck processes

MSC classifications::

• 60G40
• 60G44
• 60G51

Acknowledgements

This note was written during a stay at Heriot-Watt University, Edinburgh and I would like to express my gratitude for their hospitality and support. I also thank the referee for his/her valuable comments.