IDEAS home Printed from https://ideas.repec.org/p/ssa/lemwps/2016-13.html
   My bibliography  Save this paper

Wealth and Price Distribution by Diffusive Approximation in a Repeated Prediction Market

Author

Listed:
  • Giulio Bottazzi
  • Daniele Giachini

Abstract

The approximate agents' wealth and price invariant densities of a repeated prediction market model is derived using the Fokker-Planck equation of the associated continuous-time jump process. We show that the approximation obtained from the evolution of log-wealth difference can be reliably exploited to compute all the quantities of interest in all the acceptable parameter space. When the risk aversion of the trader is high enough, we are able to derive an explicit closed-form solution for the price distribution which is asymptotically correct.

Suggested Citation

  • Giulio Bottazzi & Daniele Giachini, 2016. "Wealth and Price Distribution by Diffusive Approximation in a Repeated Prediction Market," LEM Papers Series 2016/13, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  • Handle: RePEc:ssa:lemwps:2016/13
    as

    Download full text from publisher

    File URL: http://www.lem.sssup.it/WPLem/files/2016-13.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    2. L. C. MacLean & W. T. Ziemba & G. Blazenko, 1992. "Growth Versus Security in Dynamic Investment Analysis," Management Science, INFORMS, vol. 38(11), pages 1562-1585, November.
    3. Alina Beygelzimer & John Langford & David Pennock, 2012. "Learning Performance of Prediction Markets with Kelly Bettors," Papers 1201.6655, arXiv.org.
    4. Bottazzi, Giulio & Dindo, Pietro, 2014. "Evolution and market behavior with endogenous investment rules," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 121-146.
    5. Giulio Bottazzi & Pietro Dindo, 2015. "Drift criteria for persistence of discrete stochastic processes on the line," LEM Papers Series 2015/26, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    6. Leonard Maclean & William Ziemba & Yuming Li, 2005. "Time to wealth goals in capital accumulation," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 343-355.
    7. repec:reg:rpubli:460 is not listed on IDEAS
    8. Giulio Bottazzi & Daniele Giachini, 2016. "Far from the Madding Crowd: Collective Wisdom in Prediction Markets," LEM Papers Series 2016/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Prediction Markets; Heterogeneous Beliefs; Fractional Kelly Rule; Invariant Distribution; Diffusive Approximation; Fokker Planck Equation;

    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:ssa:lemwps:2016/13. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: () or (Rebekah McClure). General contact details of provider: http://edirc.repec.org/data/labssit.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.