IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v89y2000i1p101-116.html
   My bibliography  Save this article

Martingale representation theorems for initially enlarged filtrations

Author

Listed:
  • Amendinger, Jürgen

Abstract

In this paper we transfer martingale representation theorems from some given filtration to an initially enlarged filtration , where G is a random variable satisfying an equivalence assumption. We use then one of these theorems to solve the problem of maximizing the expected utility from both consumption and terminal wealth for an agent having the information flow at his disposal.

Suggested Citation

  • Amendinger, Jürgen, 2000. "Martingale representation theorems for initially enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 101-116, September.
    • Handle: RePEc:eee:spapps:v:89:y:2000:i:1:p:101-116
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(00)00015-6
    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. Axel Grorud & Monique Pontier, 1998. "Insider Trading in a Continuous Time Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 331-347.
    2. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    3. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    4. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    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. Huy N. Chau & Andrea Cosso & Claudio Fontana, 2018. "The value of informational arbitrage," Papers 1804.00442, arXiv.org.
    2. Ernst, Philip A. & Rogers, L.C.G. & Zhou, Quan, 2017. "The value of foresight," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3913-3927.
    3. Beatrice Acciaio & Claudio Fontana & Constantinos Kardaras, 2014. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," Papers 1401.7198, arXiv.org, revised May 2015.
    4. Fontana, Claudio, 2018. "The strong predictable representation property in initially enlarged filtrations under the density hypothesis," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 1007-1033.
    5. Bernardo D'Auria & Jos'e Antonio Salmer'on, 2017. "Valuing the anticipative information on the stochastic short interest rates," Papers 1711.03642, arXiv.org, revised Nov 2021.
    6. Peng, Xingchun & Chen, Fenge & Wang, Wenyuan, 2021. "Robust optimal investment and reinsurance for an insurer with inside information," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 15-30.
    7. Stefan Ankirchner & Steffen Dereich & Peter Imkeller, 2005. "The Shannon Information of Filtrations and the Additional Logarithmic Utility of Insiders," SFB 649 Discussion Papers SFB649DP2005-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Tahir Choulli & Sina Yansori, 2018. "Explicit description of all deflators for market models under random horizon with applications to NFLVR," Papers 1803.10128, arXiv.org, revised Feb 2021.
    9. José Manuel Corcuera & Giulia Nunno & José Fajardo, 2019. "Kyle equilibrium under random price pressure," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 77-101, June.
    10. Tahir Choulli & Sina Yansori, 2022. "Log-optimal and numéraire portfolios for market models stopped at a random time," Finance and Stochastics, Springer, vol. 26(3), pages 535-585, July.
    11. Ashkan Nikeghbali & Eckhard Platen, 2008. "On Honest Times in Financial Modeling," Research Paper Series 229, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio and num\'eraire portfolio for market models stopped at a random time," Papers 1810.12762, arXiv.org, revised Aug 2020.
    13. Peter Imkeller, 2003. "Malliavin's Calculus in Insider Models: Additional Utility and Free Lunches," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 153-169, January.
    14. Kohatsu-Higa, Arturo & Yamazato, Makoto, 2008. "Enlargement of filtrations with random times for processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1136-1158, July.
    15. Buckley, Winston S. & Brown, Garfield O. & Marshall, Mario, 2012. "A mispricing model of stocks under asymmetric information," European Journal of Operational Research, Elsevier, vol. 221(3), pages 584-592.
    16. Neda Esmaeeli & Peter Imkeller, 2015. "American Options with Asymmetric Information and Reflected BSDE," Papers 1505.05046, arXiv.org, revised Aug 2017.
    17. Claudio Fontana, 2015. "The strong predictable representation property in initially enlarged filtrations under the density hypothesis," Papers 1508.03282, arXiv.org, revised Jun 2017.
    18. Acciaio, Beatrice & Fontana, Claudio & Kardaras, Constantinos, 2016. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," LSE Research Online Documents on Economics 65150, London School of Economics and Political Science, LSE Library.
    19. Bernardo D'Auria & Jos'e Antonio Salmer'on, 2019. "Insider information and its relation with the arbitrage condition and the utility maximization problem," Papers 1909.03430, arXiv.org, revised Dec 2019.
    20. H'el`ene Halconruy, 2021. "The insider problem in the trinomial model: a discrete-time jump process approach," Papers 2106.15208, arXiv.org, revised Sep 2023.

    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:89:y:2000:i:1:p:101-116. 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.