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Affine Processes on Symmetric Cones

Author

Listed:
  • Christa Cuchiero

    (University of Vienna)

  • Martin Keller-Ressel

    (TU Dresden, Institut für Mathematische Stochastik)

  • Eberhard Mayerhofer

    (Dublin City University)

  • Josef Teichmann

    (ETH Zürich)

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.

Suggested Citation

  • Christa Cuchiero & Martin Keller-Ressel & Eberhard Mayerhofer & Josef Teichmann, 2016. "Affine Processes on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 29(2), pages 359-422, June.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0580-x
    DOI: 10.1007/s10959-014-0580-x
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    References listed on IDEAS

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    1. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    2. Christa Cuchiero & Josef Teichmann, 2011. "Path properties and regularity of affine processes on general state spaces," Papers 1107.1607, arXiv.org, revised Jan 2013.
    3. Martino Grasselli & Claudio Tebaldi, 2008. "Solvable Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 135-153, January.
    4. Hélène Massam & Erhard Neher, 1997. "On Transformations and Determinants of Wishart Variables on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 10(4), pages 867-902, October.
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    Cited by:

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    2. Benth, Fred Espen & Karbach, Sven, 2023. "Multivariate continuous-time autoregressive moving-average processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 299-337.

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