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

Madalina Deaconu 1, 2 Samuel Herrmann 3
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : In this article we investigate the hitting time of some given boundaries for Bessel processes. The main motivation is coming from mathematical finance when dealing with volatility models but the results can also be used in optimal control problems. The aim is here 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 connexion existing between Cox-Ingersoll-Ross processes and Bessel processes.
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Madalina Deaconu, Samuel Herrmann. Hitting time for Bessel processes - walk on moving spheres algorithm (WoMS). Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2013, 23 (6), pp.2259-2289. ⟨10.1214/12-AAP900⟩. ⟨hal-00636056v2⟩

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