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Ergodicity breaking in geometric Brownian motion

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  • Ole Peters
  • William Klein
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    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.

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    File URL: http://arxiv.org/pdf/1209.4517
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1209.4517.

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    Date of creation: Sep 2012
    Date of revision: Mar 2013
    Publication status: Published in Phys. Rev. Lett. 110, 100603 (2013)
    Handle: RePEc:arx:papers:1209.4517

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    Web page: http://arxiv.org/

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    Cited by:
    1. Ole Peters & Murray Gell-Mann, 2014. "Evaluating gambles using dynamics," Papers 1405.0585, arXiv.org.

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