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Affine processes on positive semidefinite d×d matrices have jumps of finite variation in dimension d>1

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  • Mayerhofer, Eberhard
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    Abstract

    The theory of affine processes on the space of positive semidefinite d×d matrices has been established in a joint work with Cuchiero et al. (2011) [4]. We confirm the conjecture stated therein that in dimension d>1 this process class does not exhibit jumps of infinite total variation. This constitutes a geometric phenomenon which is in contrast to the situation on the positive real line (Kawazu and Watanabe, 1971) [8]. As an application we prove that the exponentially affine property of the Laplace transform carries over to the Fourier–Laplace transform if the diffusion coefficient is zero or invertible.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 10 ()
    Pages: 3445-3459

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:10:p:3445-3459

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    Keywords: Affine processes; Positive semidefinite processes; Jumps; Wishart processes;

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    1. Mayerhofer, Eberhard & Pfaffel, Oliver & Stelzer, Robert, 2011. "On strong solutions for positive definite jump diffusions," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2072-2086, September.
    2. Mayerhofer, Eberhard & Muhle-Karbe, Johannes & Smirnov, Alexander G., 2011. "A characterization of the martingale property of exponentially affine processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 568-582, March.
    3. Christa Cuchiero & Damir Filipovi\'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
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    Cited by:
    1. Kang, Chulmin & Kang, Wanmo, 2013. "Transform formulae for linear functionals of affine processes and their bridges on positive semidefinite matrices," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2419-2445.

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