IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1209.4517.html
   My bibliography  Save this paper

Ergodicity breaking in geometric Brownian motion

Author

Listed:
  • Ole Peters
  • William Klein

Abstract

Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A common tactic for bringing time averages closer to ensemble averages is diversification. In this letter we study the effects of diversification using the concept of ergodicity breaking.

Suggested Citation

  • Ole Peters & William Klein, 2012. "Ergodicity breaking in geometric Brownian motion," Papers 1209.4517, arXiv.org, revised Mar 2013.
    • Handle: RePEc:arx:papers:1209.4517
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1209.4517
    File Function: Latest version
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    2. Ole Peters & Murray Gell-Mann, 2014. "Evaluating gambles using dynamics," Papers 1405.0585, arXiv.org, revised Jun 2015.
    3. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.
    4. Carlos Rodríguez Raposo & Pablo Coello Pulido, 2021. "Ergodicity transformation for additive-ruin wealth dynamic," Working Papers hal-03198073, HAL.
    5. Federica De Domenico & Giacomo Livan & Guido Montagna & Oreste Nicrosini, 2023. "Modeling and Simulation of Financial Returns under Non-Gaussian Distributions," Papers 2302.02769, arXiv.org.
    6. Ivan S. Maksymov, 2023. "Analogue and Physical Reservoir Computing Using Water Waves: Applications in Power Engineering and Beyond," Energies, MDPI, vol. 16(14), pages 1-26, July.
    7. Máté, Gabriell & Néda, Zoltán, 2016. "The advantage of inhomogeneity — Lessons from a noise driven linearized dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 310-317.
    8. Ole Peters & Alexander Adamou, 2018. "The sum of log-normal variates in geometric Brownian motion," Papers 1802.02939, arXiv.org.
    9. Simon Gluzman, 2023. "Market Crashes and Time-Translation Invariance," FinTech, MDPI, vol. 2(2), pages 1-27, March.
    10. Ole Peters & Alexander Adamou, 2015. "An evolutionary advantage of cooperation," Papers 1506.03414, arXiv.org, revised May 2018.

    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:1209.4517. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.