First Exit Times of Compound Poisson Processes with Parallel Boundaries

Abstract

We consider distributions of several first exit times of compound Poisson processes (CPPs) with positive jumps from a region that is bounded by two parallel boundaries. Recursive formulas of exact distributions are given for a CPP with absolutely continuous jumps. Non-recursive formulas are given for a CPP with discrete jumps, and are used as a numerical approximation for the absolutely continuous case. The problem has applications in queueing and risk theory as well as sequential testing.

Keywords:

• Compound Poisson process
• Linear boundaries
• Parallel boundaries
• Stopping time

Subject Classifications:

• 60G40
• 60K25
• 60J75

ACKNOWLEDGMENTS

This research is motivated by Professor S. Zacks' work. I would like to thank him for providing me with many valuable suggestions to improve this article. I am also grateful to the Editor and referees for their careful reading and helpful comments.

Notes

Recommended by Shelley Zacks