IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v29y2016i2d10.1007_s10959-014-0580-x.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-014-0580-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10959-014-0580-x?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 & Josef Teichmann, 2011. "Path properties and regularity of affine processes on general state spaces," Papers 1107.1607, arXiv.org, revised Jan 2013.
    2. Martino Grasselli & Claudio Tebaldi, 2008. "Solvable Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 135-153, January.
    3. 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.
    4. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    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. 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.
    2. Kurt, Kevin & Frey, Rüdiger, 2022. "Markov-modulated affine processes," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 391-422.

    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. 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.
    2. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.
    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.
    4. Archil Gulisashvili & Josef Teichmann, 2014. "The G\"{a}rtner-Ellis theorem, homogenization, and affine processes," Papers 1406.3716, arXiv.org.
    5. Graczyk, Piotr & Małecki, Jacek & Mayerhofer, Eberhard, 2018. "A characterization of Wishart processes and Wishart distributions," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1386-1404.
    6. Chiarella, Carl & Da Fonseca, José & Grasselli, Martino, 2014. "Pricing range notes within Wishart affine models," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 193-203.
    7. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "A general HJM framework for multiple yield curve modelling," Finance and Stochastics, Springer, vol. 20(2), pages 267-320, April.
    8. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    9. Misha Beek & Michel Mandjes & Peter Spreij & Erik Winands, 2020. "Regime switching affine processes with applications to finance," Finance and Stochastics, Springer, vol. 24(2), pages 309-333, April.
    10. Alfeus, Mesias & Grasselli, Martino & Schlögl, Erik, 2020. "A consistent stochastic model of the term structure of interest rates for multiple tenors," Journal of Economic Dynamics and Control, Elsevier, vol. 114(C).
    11. 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.
    12. repec:uts:finphd:41 is not listed on IDEAS
    13. Deelstra, Griselda & Grasselli, Martino & Van Weverberg, Christopher, 2016. "The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 205-219.
    14. Da Fonseca, José, 2024. "Pricing guaranteed annuity options in a linear-rational Wishart mortality model," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 122-131.
    15. 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.
    16. Cox, Sonja & Karbach, Sven & Khedher, Asma, 2022. "Affine pure-jump processes on positive Hilbert–Schmidt operators," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 191-229.
    17. Kurt, Kevin & Frey, Rüdiger, 2022. "Markov-modulated affine processes," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 391-422.
    18. 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.
    19. Anja Richter & Josef Teichmann, 2014. "Discrete Time Term Structure Theory and Consistent Recalibration Models," Papers 1409.1830, arXiv.org.
    20. Stefan Waldenberger & Wolfgang Muller, 2015. "Affine LIBOR models driven by real-valued affine processes," Papers 1503.00864, arXiv.org.
    21. Takashi Kato & Jun Sekine & Kenichi Yoshikawa, 2013. "Order Estimates for the Exact Lugannani-Rice Expansion," Papers 1310.3347, arXiv.org, revised Jun 2014.

    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:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0580-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.