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

Fingerprint

Market Model
Financial Markets
Limit Theorems
theorems
stochastic processes
Term
random walk
statistical mechanics
invariance
Cluster Expansion
Simple Random Walk
Invariance Principle
Scaling Limit
intervals
Statistical Mechanics
scaling
microstructure
expansion
Brownian motion
Stochastic Processes

Keywords

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

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Limit theorems in financial market models. / Kuroda, Koji; Murai, Joshin.

In: Physica A: Statistical Mechanics and its Applications, Vol. 383, No. 1 SPEC. ISS., 01.09.2007, p. 28-34.

Research output: Contribution to journalArticle

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