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A model of transaction signs with order splitting and public information

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  • Joshin Murai

    (Okayama University)

Abstract

Applying a method of the cluster expansion developed in a study of statistical mechanics, a new mathematical model has been structured to account for the reason that a time series of transaction signs in financial markets has a long memory property. A basic assumption for the model was that investors split their hidden orders into small pieces before execution. The effect of public information also was taken into consideration. A mathematical expression of investors’ investment behavior generates a discrete time stochastic process of cumulative transaction signs. The strong law of large numbers holds for the process: it converges to a trend term almost surely. The distribution of the fluctuation around the trend term weakly converges to the distribution of a superposition of a stochastic integral with respect to a Brownian motion and stochastic integrals with respect to a fractional Brownian motions with Hurst exponents greater than one-half. Namely, increments of the derived process have a long memory property.

Suggested Citation

  • Joshin Murai, 2016. "A model of transaction signs with order splitting and public information," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 469-480, December.
    • Handle: RePEc:spr:eaiere:v:13:y:2016:i:2:d:10.1007_s40844-016-0050-5
    DOI: 10.1007/s40844-016-0050-5
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Order sign; Long memory; Fractional Brownian motion;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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