IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2207.03710.html
   My bibliography  Save this paper

Non-linear Affine Processes with Jumps

Author

Listed:
  • Francesca Biagini
  • Georg Bollweg
  • Katharina Oberpriller

Abstract

We present a probabilistic construction of $\mathbb{R}^d$-valued non-linear affine processes with jumps. Given a set $\Theta$ of affine parameters, we define a family of sublinear expectations on the Skorokhod space under which the canonical process $X$ is a (sublinear) Markov process with a non-linear generator. This yields a tractable model for Knightian uncertainty for which the sublinear expectation of a Markovian functional can be calculated via a partial integro-differential equation.

Suggested Citation

  • Francesca Biagini & Georg Bollweg & Katharina Oberpriller, 2022. "Non-linear Affine Processes with Jumps," Papers 2207.03710, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:2207.03710
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2207.03710
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tolulope Fadina & Ariel Neufeld & Thorsten Schmidt, 2018. "Affine processes under parameter uncertainty," Papers 1806.02912, arXiv.org, revised Mar 2019.
    Full references (including those not matched with items on IDEAS)

    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. Criens, David & Niemann, Lars, 2024. "A class of multidimensional nonlinear diffusions with the Feller property," Statistics & Probability Letters, Elsevier, vol. 208(C).
    2. Meriam El Mansour & Emmanuel Lepinette, 2023. "Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty," Papers 2311.08847, arXiv.org.
    3. Sandrine Gumbel & Thorsten Schmidt, 2020. "Machine learning for multiple yield curve markets: fast calibration in the Gaussian affine framework," Papers 2004.07736, arXiv.org, revised Apr 2020.
    4. Blessing, Jonas & Kupper, Michael & Nendel, Max, 2023. "Convergence of Infintesimal Generators and Stability of Convex Montone Semigroups," Center for Mathematical Economics Working Papers 680, Center for Mathematical Economics, Bielefeld University.
    5. Bahar Akhtari & Francesca Biagini & Andrea Mazzon & Katharina Oberpriller, 2020. "Generalized Feynman-Kac Formula under volatility uncertainty," Papers 2012.08163, arXiv.org, revised Nov 2022.
    6. David Criens & Lars Niemann, 2022. "Robust utility maximization with nonlinear continuous semimartingales," Papers 2206.14015, arXiv.org, revised Aug 2023.
    7. Akhtari, Bahar & Biagini, Francesca & Mazzon, Andrea & Oberpriller, Katharina, 2023. "Generalized Feynman–Kac formula under volatility uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    8. Biagini, Francesca & Mazzon, Andrea & Oberpriller, Katharina, 2023. "Reduced-form framework for multiple ordered default times under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 1-43.
    9. Sandrine Gümbel & Thorsten Schmidt, 2020. "Machine Learning for Multiple Yield Curve Markets: Fast Calibration in the Gaussian Affine Framework," Risks, MDPI, vol. 8(2), pages 1-18, May.
    10. Tolulope Fadina & Thorsten Schmidt, 2024. "The Unfairness of $\varepsilon$-Fairness," Papers 2405.09360, arXiv.org, revised Jun 2024.
    11. Eva Lutkebohmert & Thorsten Schmidt & Julian Sester, 2021. "Robust deep hedging," Papers 2106.10024, arXiv.org, revised Nov 2021.
    12. Fuhrmann, Sven & Kupper, Michael & Nendel, Max, 2021. "Wasserstein Perturbations of Markovian Transition Semigroups," Center for Mathematical Economics Working Papers 649, Center for Mathematical Economics, Bielefeld University.
    13. Tolulope Fadina & Thorsten Schmidt, 2019. "Default Ambiguity," Risks, MDPI, vol. 7(2), pages 1-17, June.
    14. Criens, David & Niemann, Lars, 2024. "Markov selections and Feller properties of nonlinear diffusions," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    15. David Criens & Lars Niemann, 2023. "Robust utility maximization with nonlinear continuous semimartingales," Mathematics and Financial Economics, Springer, volume 17, number 5, December.
    16. Hölzermann, Julian, 2020. "Pricing Interest Rate Derivatives under Volatility Uncertainty," Center for Mathematical Economics Working Papers 633, Center for Mathematical Economics, Bielefeld University.
    17. Changhong Guo & Shaomei Fang & Yong He, 2023. "A Generalized Stochastic Process: Fractional G-Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-34, March.
    18. Schmidt, Thorsten & Tappe, Stefan & Yu, Weijun, 2020. "Infinite dimensional affine processes," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7131-7169.
    19. Benedikt Geuchen & Katharina Oberpriller & Thorsten Schmidt, 2022. "Affine models with path-dependence under parameter uncertainty and their application in finance," Papers 2207.13350, arXiv.org, revised Jun 2024.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:2207.03710. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.