An Elementary Approach to Optimal Stopping Problems for AR(1) Sequences

Abstract

Optimal stopping problems form a class of stochastic optimization problems that has a wide range of applications in sequential statistics and mathematical finance. Here we consider a general optimal stopping problem with discounting for autoregressive processes. Our strategy for a solution consists of two steps: First we give elementary conditions to ensure that an optimal stopping time is of threshold type. Then the resulting one-dimensional problem of finding the optimal threshold is to be solved explicitly. The second step is carried out for the case of exponentially distributed innovations.

Keywords:

• Autoregressive sequence
• Exponential innovations
• Optimal stopping
• Threshold times

2000 Mathematics Subject Classification:

• 60G40
• 62L15
• 60G99

ACKNOWLEDGMENTS

We thank the referee for valuable suggestions that improved the presentation of the article.

Notes

Recommended by T. N. Sriram