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 reallife application to a problem in hydrology is presented.

First Passage Time of a Markov Chain That Converges to Bessel Process

“…Moreover, in [5] the authors show the application of the discrete version of Cox-Ingersoll-Ross process in hydrology.…”