IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v118y2008i7p1136-1158.html
   My bibliography  Save this article

Enlargement of filtrations with random times for processes with jumps

Author

Listed:
  • Kohatsu-Higa, Arturo
  • Yamazato, Makoto

Abstract

We treat an extension of Jacod's theorem for initial enlargement of filtrations with respect to random times. In Jacod's theorem the main condition requires the absolute continuity of the conditional distribution of the random time with respect to a nonrandom measure. Examples appearing in the theory on insider trading require extensions of this theorem where the reference measure can be random. In this article we consider such an extension which leads to an extra term in the semimartingale decomposition in the enlarged filtration. Furthermore we consider a slightly modified enlargement which allows for the bounded variation part of the semimartingale decomposition to have finite moments depending on the modification considered. Various examples for Lévy processes are treated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:7:p:1136-1158
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(07)00136-6
    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. José Corcuera & Peter Imkeller & Arturo Kohatsu-Higa & David Nualart, 2004. "Additional utility of insiders with imperfect dynamical information," Finance and Stochastics, Springer, vol. 8(3), pages 437-450, August.
    4. Arturo Kohatsu‐Higa & Agnès Sulem, 2006. "Utility Maximization In An Insider Influenced Market," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 153-179, January.
    5. Imkeller, Peter & Pontier, Monique & Weisz, Ferenc, 2001. "Free lunch and arbitrage possibilities in a financial market model with an insider," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 103-130, March.
    6. Axel Grorud, 2000. "Asymmetric Information In A Financial Market With Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 641-659.
    7. 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)

    Citations

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


    Cited by:

    1. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.
    2. Cetin, Umut & Xing, Hao, 2013. "Point process bridges and weak convergence of insider trading models," LSE Research Online Documents on Economics 48745, London School of Economics and Political Science, LSE Library.
    3. Luke M. Bennett & Wei Hu, 2023. "Filtration enlargement‐based time series forecast in view of insider trading," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 112-140, February.

    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. 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.
    2. 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.
    3. Hillairet, Caroline, 2005. "Comparison of insiders' optimal strategies depending on the type of side-information," Stochastic Processes and their Applications, Elsevier, vol. 115(10), pages 1603-1627, October.
    4. José Manuel Corcuera & Giulia Di Nunno, 2018. "Kyle–Back’S Model With A Random Horizon," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-41, March.
    5. 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.
    6. Bernardo D'Auria & Jos'e Antonio Salmer'on, 2017. "Optimal portfolios with anticipating information on the stochastic interest rate," Papers 1711.03642, arXiv.org, revised Jul 2024.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Kasper Larsen & Gordan Zitkovic, 2007. "On the semimartingale property via bounded logarithmic utility," Papers 0706.0468, arXiv.org.
    12. Anne Eyraud-Loisel, 2011. "Option Hedging By An Influent Informed Investor," Post-Print hal-00450948, HAL.
    13. Ngoc Huy Chau & Wolfgang Runggaldier & Peter Tankov, 2016. "Arbitrage and utility maximization in market models with an insider," Papers 1608.02068, arXiv.org, revised Sep 2016.
    14. Kasper Larsen & Gordan Žitković, 2008. "On the semimartingale property via bounded logarithmic utility," Annals of Finance, Springer, vol. 4(2), pages 255-268, March.
    15. Aksamit, Anna & Choulli, Tahir & Deng, Jun & Jeanblanc, Monique, 2019. "No-arbitrage under additional information for thin semimartingale models," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3080-3115.
    16. Ankirchner, Stefan & Dereich, Steffen & Imkeller, Peter, 2005. "The Shannon information of filtrations and the additional logarithmic utility of insiders," SFB 649 Discussion Papers 2005-030, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    17. Acciaio, Beatrice & Fontana, Claudio & Kardaras, Constantinos, 2016. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1761-1784.
    18. 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.
    19. repec:hum:wpaper:sfb649dp2005-030 is not listed on IDEAS
    20. Jos'e Manuel Corcuera & Giulia Di Nunno & Gergely Farkas & Bernt {O}ksendal, 2014. "A continuous auction model with insiders and random time of information release," Papers 1411.2835, arXiv.org, revised Mar 2018.
    21. Huy N. Chau & Andrea Cosso & Claudio Fontana, 2018. "The value of informational arbitrage," Papers 1804.00442, arXiv.org.

    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:118:y:2008:i:7:p:1136-1158. 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.