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Pré-Publication, Document De Travail Année : 2011

A Mean-Reverting SDE on Correlation matrices

Résumé

We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a useful connection with Wishart processes that makes understand how we get the full SDE. Last, we focus on the simulation of this diffusion and present discretization schemes that achieve a second-order weak convergence.
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Dates et versions

hal-00617111 , version 1 (26-08-2011)
hal-00617111 , version 2 (13-02-2012)

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Citer

Abdelkoddousse Ahdida, Aurélien Alfonsi. A Mean-Reverting SDE on Correlation matrices. 2011. ⟨hal-00617111v1⟩

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