A model of transaction signs with order splitting and public information

Joshin Murai ()
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Joshin Murai: Okayama University

Evolutionary and Institutional Economics Review, 2016, vol. 13, issue 2, No 13, 469-480

Abstract: 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.

Keywords: Order sign; Long memory; Fractional Brownian motion (search for similar items in EconPapers)
JEL-codes: C02 C22 G10 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s40844-016-0050-5

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