IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v122y2012i10p3445-3459.html
   My bibliography  Save this article

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

Author

Listed:
  • Mayerhofer, Eberhard

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.

Suggested Citation

  • Mayerhofer, Eberhard, 2012. "Affine processes on positive semidefinite d×d matrices have jumps of finite variation in dimension d>1," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3445-3459.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:10:p:3445-3459
    DOI: 10.1016/j.spa.2012.06.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441491200124X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2012.06.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christa Cuchiero & Josef Teichmann, 2019. "Markovian lifts of positive semidefinite affine Volterra-type processes," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 407-448, December.
    2. Christa Cuchiero & Josef Teichmann, 2019. "Markovian lifts of positive semidefinite affine Volterra type processes," Papers 1907.01917, arXiv.org, revised Sep 2019.
    3. Mayerhofer, Eberhard & Stelzer, Robert & Vestweber, Johanna, 2020. "Geometric ergodicity of affine processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4141-4173.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mayerhofer, Eberhard & Stelzer, Robert & Vestweber, Johanna, 2020. "Geometric ergodicity of affine processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4141-4173.
    2. Richter, Anja, 2014. "Explicit solutions to quadratic BSDEs and applications to utility maximization in multivariate affine stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3578-3611.
    3. Da Fonseca, José, 2016. "On moment non-explosions for Wishart-based stochastic volatility models," European Journal of Operational Research, Elsevier, vol. 254(3), pages 889-894.
    4. Carlos G. Pacheco, 2016. "Picard Iterations for Diffusions on Symmetric Matrices," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1444-1457, December.
    5. Eduardo Abi Jaber & Bruno Bouchard & Camille Illand & Eduardo Abi Jaber, 2018. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Post-Print hal-01349639, HAL.
    6. Branger, Nicole & Muck, Matthias & Seifried, Frank Thomas & Weisheit, Stefan, 2017. "Optimal portfolios when variances and covariances can jump," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 59-89.
    7. Abi Jaber, Eduardo & Bouchard, Bruno & Illand, Camille, 2019. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1726-1748.
    8. Gonon, Lukas & Teichmann, Josef, 2020. "Linearized filtering of affine processes using stochastic Riccati equations," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 394-430.
    9. Friesen, Martin & Jin, Peng & Rüdiger, Barbara, 2020. "Existence of densities for multi-type continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5426-5452.
    10. Chiarella, Carl & Hsiao, Chih-Ying & Tô, Thuy-Duong, 2016. "Stochastic correlation and risk premia in term structure models," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 59-78.
    11. 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.
    12. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.
    13. Martin Keller-Ressel & Thorsten Schmidt & Robert Wardenga, 2018. "Affine processes beyond stochastic continuity," Papers 1804.07556, arXiv.org, revised Dec 2018.
    14. Nicole Branger & Matthias Muck & Stefan Weisheit, 2019. "Correlation risk and international portfolio choice," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 128-146, January.
    15. Eduardo Abi Jaber & Bruno Bouchard & Camille Illand & Eduardo Jaber, 2018. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Working Papers hal-01349639, HAL.
    16. 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.
    17. Eduardo Abi Jaber, 2022. "The Laplace transform of the integrated Volterra Wishart process," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 309-348, January.
    18. Chulmin Kang & Wanmo Kang & Jong Mun Lee, 2017. "Exact Simulation of the Wishart Multidimensional Stochastic Volatility Model," Operations Research, INFORMS, vol. 65(5), pages 1190-1206, October.
    19. Harms, Philipp & Stefanovits, David, 2019. "Affine representations of fractional processes with applications in mathematical finance," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1185-1228.
    20. Sebastien Valeyre, 2020. "Refined model of the covariance/correlation matrix between securities," Papers 2001.08911, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:122:y:2012:i:10:p:3445-3459. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.