Limit theorems in financial market models

Koji Kuroda, Joshin Murai

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Invariance principle states that a scaled simple random walk converges to the standard Brownian motion. In this article, we present a discrete time stochastic process, which reflects a microstructure of market dynamics, and prove a convergence to a scaling limit process with a drift term and a jump term. These terms are derived from a macroscopic condition on volumes traded in some time intervals. The mathematical tools for obtaining our results are Dobrushin-Hryniv theory and the method of cluster expansion developed in mathematical studies of statistical mechanics.

Original languageEnglish
Pages (from-to)28-34
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume383
Issue number1 SPEC. ISS.
DOIs
Publication statusPublished - Sep 1 2007

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Keywords

  • Cluster expansion
  • Continuous double auction
  • Dobrushin-Hryniv theory
  • Drift coefficient
  • Jump process

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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