IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v101y2002i2p273-302.html
   My bibliography  Save this article

Stochastic targets with mixed diffusion processes and viscosity solutions

Author

Listed:
  • Bouchard, Bruno

Abstract

Let Zt,z[nu] be a -valued mixed diffusion process controlled by [nu] with initial condition Zt,z[nu](t)=z. In this paper, we characterize the set of initial conditions such that Zt,z[nu] can be driven above a given stochastic target at time T by proving that the corresponding value function is a discontinuous viscosity solution of a variational partial differential equation. As applications of our main result, we study two examples: a problem of optimal insurance under self-protection and a problem of option hedging under jumping stochastic volatility where the underlying stock pays a random dividend at a fixed date.

Suggested Citation

  • Bouchard, Bruno, 2002. "Stochastic targets with mixed diffusion processes and viscosity solutions," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 273-302, October.
    • Handle: RePEc:eee:spapps:v:101:y:2002:i:2:p:273-302
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(02)00129-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    2. repec:dau:papers:123456789/1533 is not listed on IDEAS
    3. Touzi, Nizar, 2000. "Direct characterization of the value of super-replication under stochastic volatility and portfolio constraints," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 305-328, August.
    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. Marc Abeille & Bruno Bouchard & Lorenzo Croissant, 2023. "Diffusive Limit Approximation of Pure-Jump Optimal Stochastic Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 147-176, January.
    2. Erhan Bayraktar & Jiaqi Li, 2016. "Stochastic Perron for Stochastic Target Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1026-1054, September.

    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. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    2. Philippe Bich & Rida Laraki, 2017. "Externalities in Economies with Endogenous Sharing Rules," PSE-Ecole d'économie de Paris (Postprint) halshs-01437507, HAL.
    3. Dutta, Rohan & Levine, David Knudsen & Modica, Salvatore, 2018. "Collusion constrained equilibrium," Theoretical Economics, Econometric Society, vol. 13(1), January.
    4. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2018. "Sufficient conditions for weak reciprocal upper semi-continuity in mixed extensions of games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 99-107.
    5. Oriol Carbonell-Nicolau, 2021. "Equilibria in infinite games of incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 311-360, June.
    6. Philippe Bich & Rida Laraki, 2015. "Abstract Economies with Endogenous Sharing Rules," Documents de travail du Centre d'Economie de la Sorbonne 15058, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Pak Hung Au & Mark Whitmeyer, 2018. "Attraction versus Persuasion: Information Provision in Search Markets," Papers 1802.09396, arXiv.org, revised May 2022.
    8. Paulo k. Monteiro & Jaime Orrillo & Rudy Rosas, 2019. "Hyperopic Topologies Once Again," Economics Bulletin, AccessEcon, vol. 39(4), pages 2706-2710.
    9. Bajoori, Elnaz & Flesch, János & Vermeulen, Dries, 2016. "Behavioral perfect equilibrium in Bayesian games," Games and Economic Behavior, Elsevier, vol. 98(C), pages 78-109.
    10. Holmberg, Pär & Newbery, David & Ralph, Daniel, 2013. "Supply function equilibria: Step functions and continuous representations," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1509-1551.
    11. Guilherme Carmona, 2011. "Symposium on: Existence of Nash equilibria in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 1-4, September.
    12. Pálvölgyi, Dénes & Peters, Hans & Vermeulen, Dries, 2014. "A strategic approach to multiple estate division problems," Games and Economic Behavior, Elsevier, vol. 88(C), pages 135-152.
    13. Michele Piccione & Ran Spiegler, 2012. "Price Competition Under Limited Comparability," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(1), pages 97-135.
    14. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Working Papers halshs-01337293, HAL.
    15. Rabia Nessah & Guoqiang Tian, 2013. "Existence of Solution of Minimax Inequalities, Equilibria in Games and Fixed Points Without Convexity and Compactness Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 75-95, April.
    16. Jonathan Vogel, 2008. "Spatial Competition with Heterogeneous Firms," Journal of Political Economy, University of Chicago Press, vol. 116(3), pages 423-466, June.
    17. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    18. Pär Holmberg, 2017. "Pro‐competitive Rationing in Multi‐unit Auctions," Economic Journal, Royal Economic Society, vol. 127(605), pages 372-395, October.
    19. Prokopovych, Pavlo & Yannelis, Nicholas C., 2017. "On strategic complementarities in discontinuous games with totally ordered strategies," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 147-153.
    20. Erik Balder, 2011. "An equilibrium closure result for discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 47-65, September.

    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:101:y:2002:i:2:p:273-302. 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.