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A self-equilibrium Friedman-like urn via stochastic approximation

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  • Gao, Shuyang
  • Mahmoud, Hosam M.

Abstract

In this study, we propose a class of generalized Friedman urns with random entries. The class has the property of self-equilibrium. We prove the almost-sure convergence to the equilibrium point of this entire class by the method of stochastic approximation. We develop a central limit theorem for the proportion of white balls through the convergence theorem of stochastic approximation algorithms. We then apply this class of schemes to model the effect of trading on the price in the stock market under the efficient market hypothesis.

Suggested Citation

  • Gao, Shuyang & Mahmoud, Hosam M., 2018. "A self-equilibrium Friedman-like urn via stochastic approximation," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 77-83.
    • Handle: RePEc:eee:stapro:v:142:y:2018:i:c:p:77-83
    DOI: 10.1016/j.spl.2018.07.006
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    References listed on IDEAS

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    1. Conrad, Jennifer & Kaul, Gautam, 1998. "An Anatomy of Trading Strategies," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 489-519.
    2. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    3. J. Michael Harrison & David M. Kreps, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(2), pages 323-336.
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    Cited by:

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