IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v336y2024i1d10.1007_s10479-022-05060-0.html
   My bibliography  Save this article

Anticipative information in a Brownian−Poisson market

Author

Listed:
  • Bernardo D’Auria

    (University of Padova)

  • Jose A. Salmeron

    (University Carlos III of Madrid)

Abstract

The anticipative information refers to some information about future events that may be disclosed in advance. This information may regard, for example, financial assets and their future trends. In our paper, we assume the existence of some anticipative information in a market whose risky asset dynamics evolve according to a Brownian motion and a Poisson process. Using Malliavin calculus and filtration enlargement techniques, we derive the information drift of the mentioned processes and, both in the pure jump case and in the mixed one, we compute the additional expected logarithmic utility. Many examples are shown, where the anticipative information is related to some conditions that the constituent processes or their running maximum may verify, in particular, we show new examples considering Bernoulli random variables.

Suggested Citation

  • Bernardo D’Auria & Jose A. Salmeron, 2024. "Anticipative information in a Brownian−Poisson market," Annals of Operations Research, Springer, vol. 336(1), pages 1289-1314, May.
    • Handle: RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-022-05060-0
    DOI: 10.1007/s10479-022-05060-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-022-05060-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-022-05060-0?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

    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. Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "The value of knowing the market price of risk," Annals of Operations Research, Springer, vol. 299(1), pages 101-131, April.
    5. Hans‐Peter Bermin, 2002. "A General Approach to Hedging Options: Applications to Barrier and Partial Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 199-218, July.
    6. Ankirchner, Stefan, 2008. "On filtration enlargements and purely discontinuous martingales," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1662-1678, September.
    7. 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.
    8. 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.
    9. Josep Vives & Jorge A. León & Frederic Utzet & Josep L. Solé, 2002. "On Lévy processes, Malliavin calculus and market models with jumps," Finance and Stochastics, Springer, vol. 6(2), pages 197-225.
    10. 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.
    11. Giulia Di Nunno & Thilo Meyer-Brandis & Bernt Øksendal & Frank Proske, 2006. "Optimal portfolio for an insider in a market driven by Levy processes," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 83-94.
    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. D'Auria, Bernardo & Salmerón Garrido, José Antonio, 2021. "Anticipative information in a Brownian-Poisson market: the binary information," DES - Working Papers. Statistics and Econometrics. WS 33624, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Bernardo D'Auria & Jos'e A. Salmer'on, 2021. "Anticipative information in a Brownian-Poissonmarket: the binary information," Papers 2111.01529, arXiv.org.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Kasper Larsen & Gordan Zitkovic, 2007. "On the semimartingale property via bounded logarithmic utility," Papers 0706.0468, arXiv.org.
    13. Anne Eyraud-Loisel, 2011. "Option Hedging By An Influent Informed Investor," Post-Print hal-00450948, HAL.
    14. 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.
    15. Kasper Larsen & Gordan Žitković, 2008. "On the semimartingale property via bounded logarithmic utility," Annals of Finance, Springer, vol. 4(2), pages 255-268, March.
    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. Olfa Draouil & Bernt {O}ksendal, 2018. "Viable Insider Markets," Papers 1801.03720, arXiv.org.
    19. 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.
    20. repec:hum:wpaper:sfb649dp2005-030 is not listed on IDEAS
    21. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-022-05060-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.