IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-02879222.html

The use of BSDEs to characterize the mean–variance hedging problem and the variance optimal martingale measure for defaultable claims

Author

Listed:
  • Stéphane Goutte

    (LED - Laboratoire d'Economie Dionysien - UP8 - Université Paris 8)

  • Armand Ngoupeyou

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we consider the problem of mean-variance hedging of a defaultable claim. We assume the underlying assets are jump processes driven by Brownian motion and default processes. Using the dynamic programming principle, we link the existence of the solution of the mean-variance hedging problem to the existence of solution of a system of coupled backward stochastic differential equations (BSDEs). First we prove the existence of a solution to this system of coupled BSDEs. Then we give the corresponding solution to the mean variance hedging problem. Finally, we give some existence conditions and characterize the well known variance optimal martingale measure (VOMM) using the solution to the first quadratic BSDE with jumps that we derived from the previous stochastic control problem. We conclude with an explicit example of our credit risk model giving a numerical application in a two defaults case

Suggested Citation

  • Stéphane Goutte & Armand Ngoupeyou, 2015. "The use of BSDEs to characterize the mean–variance hedging problem and the variance optimal martingale measure for defaultable claims," Post-Print hal-02879222, HAL.
    • Handle: RePEc:hal:journl:hal-02879222
    DOI: 10.1016/j.spa.2014.10.017
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    Other versions of this item:

    Citations

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


    Cited by:

    1. Abid, Ilyes & Dhaoui, Abderrazak & Goutte, Stéphane & Guesmi, Khaled, 2019. "Contagion and bond pricing: The case of the ASEAN region," Research in International Business and Finance, Elsevier, vol. 47(C), pages 371-385.
    2. Tetsuya Ishikawa & Scott Robertson, 2017. "Optimal Investment and Pricing in the Presence of Defaults," Papers 1703.00062, arXiv.org.

    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:hal:journl:hal-02879222. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.