On a discrete version of the CIR process

Abstract

We consider the so-called gambler's ruin problem for a discrete-time Markov chain that converges to a Cox–Ingersoll–Ross (CIR) process. Both the probability that the chain will hit a given boundary before the other and the average number of transitions needed to end the game are computed explicitly. Furthermore, we show that the quantities that we obtained tend to the corresponding ones for the CIR process. A real-life application to a problem in hydrology is presented.

Keywords:

• discrete-time Markov chains
• financial mathematics
• diffusion processes
• absorption problems
• hydrology

Keywords:

• 39A60
• 60J10
• 60J60
• 60J70

Acknowledgement

The authors are grateful to the anonymous reviewers for their constructive comments.

Notes

1. [email protected].

Additional information

Notes on contributors

Moussa Kounta

1