On Minimax Duality in Optimal Stopping

Abstract

In this article we relate the two following results: The multiplicative minimax duality formula in optimal stopping introduced by Jamshidian (2007, Stochastics 79: 27–60) and the martingale approach to optimal stopping introduced by Beibel and Lerche (1997, Statistica Sinica 7: 93–108). We obtain a minimax duality formula (3.4) similar to Jamshidian's one and discuss some related questions.

Keywords:

• Jamshidian's multiplicative minimax duality
• Martingale approach of Beibel and Lerche
• Optimal stopping
• Snell envelope

Subject Classification:

• 60G40
• 62C10
• 62L15

ACKNOWLEDGMENTS

The authors are grateful to F. Jamshidian for helpful discussions and valuable suggestions. This article was written while the second author was a research fellow of the Alexander von Humboldt-Stiftung at the University of Freiburg, Germany. He thanks the Foundation for the support.

Notes

Recommended by A. G. Tartakovsky