Application of the Cluster Expansion to a Mathematical Model of the Long Memory Phenomenon in a Financial Market

Koji Kuroda, Jun ichi Maskawa, Joshin Murai

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Empirical studies of the high frequency data in stock markets show that the time series of trade signs or signed volumes has a long memory property. In this paper, we present a discrete time stochastic process for polymer model which describes trader's trading strategy, and show that a scale limit of the process converges to superposition of fractional Brownian motions with Hurst exponents Hm >1/2 and Brownian motion, provided that the index γ of the time scale about the trader's investment strategy coincides with the index δ of the interaction range in the discrete time process. The main tool for the investigation is the method of cluster expansion developed in the mathematical study of statistical mechanics.

Original languageEnglish
Pages (from-to)706-723
Number of pages18
JournalJournal of Statistical Physics
Volume152
Issue number4
DOIs
Publication statusPublished - Aug 1 2013

Keywords

  • Cluster expansion
  • Fractional Brownian motion
  • Long memory
  • Scaling limit

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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