Affine Processes on Symmetric Cones

Christa Cuchiero (), Martin Keller-Ressel (), Eberhard Mayerhofer () and Josef Teichmann ()
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Christa Cuchiero: University of Vienna
Martin Keller-Ressel: TU Dresden, Institut für Mathematische Stochastik
Eberhard Mayerhofer: Dublin City University
Josef Teichmann: ETH Zürich

Journal of Theoretical Probability, 2016, vol. 29, issue 2, 359-422

Abstract: Abstract We consider affine Markov processes taking values in convex cones. In particular, we characterize all affine processes taking values in irreducible symmetric cones in terms of certain Lévy–Khintchine triplets. This is the natural, coordinate-free formulation of the theory of Wishart processes on positive semidefinite matrices, as put forward by Bru (J Theor Probab 4(4):725–751, 1991) and Cuchiero et al. (Ann Appl Probab 21(2):397–463, 2011), in the more general context of symmetric cones, which also allows for simpler, alternative proofs.

Keywords: Affine processes; Symmetric cones; Non-central Wishart distribution; Wishart processes; Primary: 60J25; Secondary: 15B48 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-014-0580-x

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