IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1508.06376.html
   My bibliography  Save this paper

A white noise approach to insider trading

Author

Listed:
  • Bernt {O}ksendal
  • Elin R{o}se

Abstract

We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, Hida-Malliavin calculus and the Donsker delta function.

Suggested Citation

  • Bernt {O}ksendal & Elin R{o}se, 2015. "A white noise approach to insider trading," Papers 1508.06376, arXiv.org.
    • Handle: RePEc:arx:papers:1508.06376
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1508.06376
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jan Ubøe & Bernt Øksendal & Knut Aase & Nicolas Privault, 2000. "White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance," Finance and Stochastics, Springer, vol. 4(4), pages 465-496.
    2. Monique Jeanblanc & Marc Yor & Marc Chesney, 2010. "Mathematical Methods for Financial Markets," Finance, Presses universitaires de Grenoble, vol. 31(1), pages 81-85.
    3. Russo, Francesco & Vallois, Pierre, 1995. "The generalized covariation process and Ito formula," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 81-104, September.
    4. 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. Olfa Draouil & Bernt {O}ksendal, 2018. "Viable Insider Markets," Papers 1801.03720, arXiv.org.
    2. Beghin, Luisa & Cristofaro, Lorenzo & Mishura, Yuliya, 2024. "A class of processes defined in the white noise space through generalized fractional operators," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    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. Almada Monter, Sergio Angel, 2015. "Quadratic covariation estimates in non-smooth stochastic calculus," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 343-361.
    5. Markus Hess, 2019. "Optimal Equivalent Probability Measures under Enlarged Filtrations," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 813-839, December.
    6. Bouchard, Bruno & Loeper, Grégoire & Tan, Xiaolu, 2022. "A ℂ0,1-functional Itô’s formula and its applications in mathematical finance," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 299-323.
    7. 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.
    8. N. Naguez & J. L. Prigent, 2017. "Optimal portfolio positioning within generalized Johnson distributions," Quantitative Finance, Taylor & Francis Journals, vol. 17(7), pages 1037-1055, July.
    9. Blandine, Bérard Bergery & Pierre, Vallois, 2008. "Approximation via regularization of the local time of semimartingales and Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2058-2070, November.
    10. Matteo Ludovico Bedini & Rainer Buckdahn & Hans-Jurgen Engelbert, 2016. "Unexpected Default in an Information Based Model," Papers 1611.02952, arXiv.org.
    11. Errami, Mohammed & Russo, Francesco, 2003. "n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 259-299, April.
    12. Aase, Knut K., 2004. "The perpetual American put option for jump-diffusions: Implications for equity premiums," Discussion Papers 2004/19, Norwegian School of Economics, Department of Business and Management Science.
    13. Hu, Yaozhong & Øksendal, Bernt, 2019. "Linear Volterra backward stochastic integral equations," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 626-633.
    14. Wei Chen, 2013. "Fractional G-White Noise Theory, Wavelet Decomposition for Fractional G-Brownian Motion, and Bid-Ask Pricing Application to Finance Under Uncertainty," Papers 1306.4070, arXiv.org.
    15. Leão, Dorival & Ohashi, Alberto, 2010. "Weak Approximations for Wiener Functionals," Insper Working Papers wpe_215, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    16. Matteo Ludovico Bedini & Rainer Buckdahn & Hans-Jurgen Engelbert, 2016. "Brownian Bridges on Random Intervals," Papers 1601.01811, arXiv.org.
    17. Aase, Knut K., 2005. "Using Option Pricing Theory to Infer About Equity Premiums," Discussion Papers 2005/11, Norwegian School of Economics, Department of Business and Management Science.
    18. Suzuki, Ryoichi, 2018. "Malliavin differentiability of indicator functions on canonical Lévy spaces," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 183-190.
    19. Goldys, Beniamin & Wu, Wei, 2019. "On a class of singular stochastic control problems driven by Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3174-3206.
    20. Füss, Roland & Mahringer, Steffen & Prokopczuk, Marcel, 2015. "Electricity derivatives pricing with forward-looking information," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 34-57.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1508.06376. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.