## The Annals of Applied Probability

### Hitting time for Bessel processes—walk on moving spheres algorithm (WoMS)

#### Abstract

In this article we investigate the hitting time of some given boundaries for Bessel processes. The main motivation comes from mathematical finance when dealing with volatility models, but the results can also be used in optimal control problems. The aim here is to construct a new and efficient algorithm in order to approach this hitting time. As an application we will consider the hitting time of a given level for the Cox–Ingersoll–Ross process. The main tools we use are on one side, an adaptation of the method of images to this particular situation and on the other side, the connection that exists between Cox–Ingersoll–Ross processes and Bessel processes.

#### Article information

Source
Ann. Appl. Probab., Volume 23, Number 6 (2013), 2259-2289.

Dates
First available in Project Euclid: 22 October 2013

https://projecteuclid.org/euclid.aoap/1382447688

Digital Object Identifier
doi:10.1214/12-AAP900

Mathematical Reviews number (MathSciNet)
MR3127935

Zentralblatt MATH identifier
1298.65018

#### Citation

Deaconu, Madalina; Herrmann, Samuel. Hitting time for Bessel processes—walk on moving spheres algorithm (WoMS). Ann. Appl. Probab. 23 (2013), no. 6, 2259--2289. doi:10.1214/12-AAP900. https://projecteuclid.org/euclid.aoap/1382447688

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