IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1208.0763.html
   My bibliography  Save this paper

Second Order BSDEs with Jumps: Existence and probabilistic representation for fully-nonlinear PIDEs

Author

Listed:
  • M. Nabil Kazi-Tani
  • Dylan Possamai
  • Chao Zhou

Abstract

In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJs for short) started in our accompanying paper [15]. We prove existence of these equations by a direct method, thus providing complete wellposedness for 2BSDEJs. These equations are a natural candidate for the probabilistic interpretation of some fully non-linear partial integro-differential equations, which is the point of the second part of this work. We prove a non-linear Feynman-Kac formula and show that solutions to 2BSDEJs provide viscosity solutions of the associated PIDEs.

Suggested Citation

  • M. Nabil Kazi-Tani & Dylan Possamai & Chao Zhou, 2012. "Second Order BSDEs with Jumps: Existence and probabilistic representation for fully-nonlinear PIDEs," Papers 1208.0763, arXiv.org, revised May 2014.
    • Handle: RePEc:arx:papers:1208.0763
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1208.0763
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    2. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
    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. Dylan Possamai & Guillaume Royer & Nizar Touzi, 2013. "On the Robust superhedging of measurable claims," Papers 1302.1850, arXiv.org, revised Feb 2013.

    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. Andrew Papanicolaou, 2018. "Backward SDEs for Control with Partial Information," Papers 1807.08222, arXiv.org.
    2. Thai Nguyen & Mitja Stadje, 2020. "Utility maximization under endogenous pricing," Papers 2005.04312, arXiv.org, revised Mar 2024.
    3. Zixin Feng & Dejian Tian, 2021. "Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints," Papers 2111.09032, arXiv.org, revised May 2023.
    4. Jessica Martin & Stéphane Villeneuve, 2021. "A Class of Explicit optimal contracts in the face of shutdown," Working Papers hal-03124102, HAL.
    5. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Post-Print hal-04164688, HAL.
    6. Guanxing Fu & Xizhi Su & Chao Zhou, 2020. "Mean Field Exponential Utility Game: A Probabilistic Approach," Papers 2006.07684, arXiv.org, revised Jul 2020.
    7. Wahid Faidi, 2022. "Optimal investment and consumption under logarithmic utility and uncertainty model," Papers 2211.05367, arXiv.org.
    8. Martin, Jessica & Villeneuve, Stéphane, 2021. "A Class of Explicit optimal contracts in the face of shutdown," TSE Working Papers 21-1183, Toulouse School of Economics (TSE), revised Apr 2022.
    9. Thibaut Mastrolia, 2017. "Moral hazard in welfare economics: on the advantage of Planner's advices to manage employees' actions," Papers 1706.01254, arXiv.org.
    10. Mastrolia, Thibaut, 2018. "Density analysis of non-Markovian BSDEs and applications to biology and finance," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 897-938.
    11. M. Nabil Kazi-Tani & Dylan Possamai & Chao Zhou, 2014. "Quadratic BSDEs with jumps: related non-linear expectations," Papers 1403.2730, arXiv.org.
    12. Grzegorz Hara'nczyk & Wojciech S{l}omczy'nski & Tomasz Zastawniak, 2007. "Relative and Discrete Utility Maximising Entropy," Papers 0709.1281, arXiv.org.
    13. Monique Jeanblanc & Thibaut Mastrolia & Dylan Possamaï & Anthony Réveillac, 2015. "Utility Maximization With Random Horizon: A Bsde Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-43, November.
    14. Huyên Pham & Xiaoli Wei & Chao Zhou, 2022. "Portfolio diversification and model uncertainty: A robust dynamic mean‐variance approach," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 349-404, January.
    15. Thibaut Mastrolia, 2017. "Moral hazard in welfare economics: on the advantage of Planner's advices to manage employees' actions," Working Papers hal-01504473, HAL.
    16. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
    17. Horst, Ulrich & Hu, Ying & Imkeller, Peter & Réveillac, Anthony & Zhang, Jianing, 2014. "Forward–backward systems for expected utility maximization," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1813-1848.
    18. Giuseppe Benedetti & Luciano Campi, 2013. "Utility indifference valuation for non-smooth payoffs with an application to power derivatives," Papers 1307.4591, arXiv.org.
    19. Marina Santacroce & Paola Siri & Barbara Trivellato, 2023. "Forward Backward SDEs Systems for Utility Maximization in Jump Diffusion Models," Papers 2302.08253, arXiv.org.
    20. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 1-43, June.

    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:1208.0763. 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.