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Jarzynski-type equalities in gambling: role of information in capital growth

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  • Yuji Hirono
  • Yoshimasa Hidaka

Abstract

We study the capital growth in gambling with (and without) side information and memory effects. We derive several equalities for gambling, which are of similar form to the Jarzynski equality and its extension to systems with feedback controls. Those relations provide us with new measures to quantify the effects of information on the statistics of capital growth in gambling. We discuss the implications of the equalities and show that they reproduce the known upper bounds of average capital growth rates.

Suggested Citation

  • Yuji Hirono & Yoshimasa Hidaka, 2015. "Jarzynski-type equalities in gambling: role of information in capital growth," Papers 1505.06216, arXiv.org, revised Aug 2015.
    • Handle: RePEc:arx:papers:1505.06216
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    File URL: http://arxiv.org/pdf/1505.06216
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    Cited by:

    1. L'eo Touzo & Matteo Marsili & Don Zagier, 2020. "Information thermodynamics of financial markets: the Glosten-Milgrom model," Papers 2010.01905, arXiv.org, revised Jan 2021.

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