The Annals of Applied Probability

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

Madalina Deaconu and Samuel Herrmann

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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.

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

First available in Project Euclid: 22 October 2013

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Primary: 65C20: Models, numerical methods [See also 68U20] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]

Bessel processes Cox–Ingersoll–Ross processes hitting time method of images numerical algorithm


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.

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