IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2108.04047.html
   My bibliography  Save this paper

Reduced-form framework for multiple ordered default times under model uncertainty

Author

Listed:
  • Francesca Biagini
  • Andrea Mazzon
  • Katharina Oberpriller

Abstract

In this paper we introduce a sublinear conditional operator with respect to a family of possibly nondominated probability measures in presence of multiple ordered default times. In this way we generalize the results of [5], where a reduced-form framework under model uncertainty for a single default time is developed. Moreover, we use this operator for the valuation of credit portfolio derivatives under model uncertainty.

Suggested Citation

  • Francesca Biagini & Andrea Mazzon & Katharina Oberpriller, 2021. "Reduced-form framework for multiple ordered default times under model uncertainty," Papers 2108.04047, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:2108.04047
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2108.04047
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jakob Sidenius & Vladimir Piterbarg & Leif Andersen, 2008. "A New Framework For Dynamic Credit Portfolio Loss Modelling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 163-197.
    2. Acciaio, Beatrice & Larsson, Martin, 2017. "Semi-static completeness and robust pricing by informed investors," LSE Research Online Documents on Economics 68502, London School of Economics and Political Science, LSE Library.
    3. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem for Continuous Processes," Post-Print hal-01076062, HAL.
    4. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
    5. Ariel Neufeld & Marcel Nutz, 2015. "Robust Utility Maximization with L\'evy Processes," Papers 1502.05920, arXiv.org, revised Mar 2016.
    6. Soner, H. Mete & Touzi, Nizar & Zhang, Jianfeng, 2011. "Martingale representation theorem for the G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 265-287, February.
    7. Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
    8. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem For Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 963-987, October.
    9. Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2015. "Density approach in modelling successive defaults," Post-Print hal-00870492, HAL.
    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. 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.
    2. Felix-Benedikt Liebrich & Marco Maggis & Gregor Svindland, 2020. "Model Uncertainty: A Reverse Approach," Papers 2004.06636, arXiv.org, revised Mar 2022.
    3. Thibaut Mastrolia & Dylan Possamaï, 2018. "Moral Hazard Under Ambiguity," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 452-500, November.
    4. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
    5. Francesca Biagini & Katharina Oberpriller, 2020. "Reduced-form setting under model uncertainty with non-linear affine processes," Papers 2006.14307, arXiv.org, revised Jun 2020.
    6. Julian Holzermann, 2020. "Pricing Interest Rate Derivatives under Volatility Uncertainty," Papers 2003.04606, arXiv.org, revised Nov 2021.
    7. Yu‐Jui Huang & Xiang Yu, 2021. "Optimal stopping under model ambiguity: A time‐consistent equilibrium approach," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 979-1012, July.
    8. Hölzermann, Julian, 2020. "Pricing Interest Rate Derivatives under Volatility Uncertainty," Center for Mathematical Economics Working Papers 633, Center for Mathematical Economics, Bielefeld University.
    9. Francesca Biagini & Yinglin Zhang, 2017. "Reduced-form framework under model uncertainty," Papers 1707.04475, arXiv.org, revised Mar 2018.
    10. Bruno Bouchard & Xiaolu Tan, 2021. "A quasi-sure optional decomposition and super-hedging result on the Skorokhod space," Finance and Stochastics, Springer, vol. 25(3), pages 505-528, July.
    11. Johannes Muhle-Karbe & Marcel Nutz, 2018. "A risk-neutral equilibrium leading to uncertain volatility pricing," Finance and Stochastics, Springer, vol. 22(2), pages 281-295, April.
    12. Marcel Nutz, 2013. "Utility Maximization under Model Uncertainty in Discrete Time," Papers 1307.3597, arXiv.org.
    13. Daniel Bartl & Michael Kupper & David J. Prömel & Ludovic Tangpi, 2019. "Duality for pathwise superhedging in continuous time," Finance and Stochastics, Springer, vol. 23(3), pages 697-728, July.
    14. Francesca Biagini & Jacopo Mancin, 2016. "Robust Financial Bubbles," Papers 1602.05471, arXiv.org.
    15. Liu, Guomin, 2020. "Exit times for semimartingales under nonlinear expectation," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7338-7362.
    16. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2018. "Dynamic programming approach to principal–agent problems," Finance and Stochastics, Springer, vol. 22(1), pages 1-37, January.
    17. Marcel Nutz, 2014. "Robust Superhedging with Jumps and Diffusion," Papers 1407.1674, arXiv.org, revised Jul 2015.
    18. Erhan Bayraktar & Alexander Munk, 2014. "Comparing the $G$-Normal Distribution to its Classical Counterpart," Papers 1407.5139, arXiv.org, revised Dec 2014.
    19. Matteo Burzoni & Marco Maggis, 2019. "Arbitrage-free modeling under Knightian Uncertainty," Papers 1909.04602, arXiv.org, revised Apr 2020.
    20. Ludovic Tangpi, 2018. "Efficient hedging under ambiguity in continuous time," Papers 1812.10876, arXiv.org, revised Mar 2019.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:2108.04047. 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.