IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v122y2012i7p2668-2700.html
   My bibliography  Save this article

Stochastic variational inequalities with oblique subgradients

Author

Listed:
  • Gassous, Anouar M.
  • Răşcanu, Aurel
  • Rotenstein, Eduard

Abstract

In this paper we will study the existence and uniqueness of the solution for the stochastic variational inequality with oblique subgradients of the following form: {dXt+H(Xt)∂φ(Xt)(dt)∋f(t,Xt)dt+g(t,Xt)dBt,t>0,X0=x∈Dom(φ)¯. Here, the mixture between the monotonicity property of the subdifferential operator ∂φ and the Lipschitz property of the matrix mapping X⟼H(X) leads to stronger difficulties in comparison to the classical case of stochastic variational inequalities. The existence result is based on a deterministic approach: a differential system with singular input is first analyzed.

Suggested Citation

  • Gassous, Anouar M. & Răşcanu, Aurel & Rotenstein, Eduard, 2012. "Stochastic variational inequalities with oblique subgradients," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2668-2700.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:7:p:2668-2700
    DOI: 10.1016/j.spa.2012.04.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441491200083X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2012.04.012?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. Rozkosz, Andrzej & Slominski, Leszek, 1997. "On stability and existence of solutions of SDEs with reflection at the boundary," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 285-302, June.
    2. Ramasubramanian, S., 2006. "An insurance network: Nash equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 374-390, 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. Zălinescu, Adrian, 2014. "Stochastic variational inequalities with jumps," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 785-811.
    2. Gassous, Anouar M. & Răşcanu, Aurel & Rotenstein, Eduard, 2015. "Multivalued backward stochastic differential equations with oblique subgradients," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3170-3195.

    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. Offer Kella & S. Ramasubramanian, 2012. "Asymptotic Irrelevance of Initial Conditions for Skorohod Reflection Mapping on the Nonnegative Orthant," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 301-312, May.
    2. Semrau-Giłka, Alina, 2015. "On approximation of solutions of one-dimensional reflecting SDEs with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 315-321.
    3. Adams, Daniel & dos Reis, Gonçalo & Ravaille, Romain & Salkeld, William & Tugaut, Julian, 2022. "Large Deviations and Exit-times for reflected McKean–Vlasov equations with self-stabilising terms and superlinear drifts," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 264-310.
    4. I. Venkat Appal Raju & S. Ramasubramanian, 2016. "Risk Diversifying Treaty Between Two Companies with Only One in Insurance Business," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 183-214, November.
    5. Wu, Yang-Che, 2020. "Equilibrium in natural catastrophe insurance market under disaster-resistant technologies, financial innovations and government interventions," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 116-128.
    6. Masanori Hino & Kouhei Matsuura & Misaki Yonezawa, 2021. "Pathwise Uniqueness and Non-explosion Property of Skorohod SDEs with a Class of Non-Lipschitz Coefficients and Non-smooth Domains," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2166-2191, December.
    7. Słomiński, Leszek, 2013. "Weak and strong approximations of reflected diffusions via penalization methods," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 752-763.
    8. Chorowski, Jakub & Trabs, Mathias, 2016. "Spectral estimation for diffusions with random sampling times," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 2976-3008.

    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:eee:spapps:v:122:y:2012:i:7:p:2668-2700. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.