A limit theorem for financial markets with inert investors

Erhan Bayraktar, Ulrich Horst, Ronnie Sircar

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling inert investors. With a suitable scaling, we show that when the price is driven by the market imbalance, the log price process is approximated by a process with long-range dependence and non-Gaussian returns distributions, driven by a fractional Brownian motion. Consequently, investor inertia may lead to arbitrage opportunities for sophisticated market participants. The mathematical contributions are a functional central limit theorem for stationary semi-Markov processes and approximation results for stochastic integrals of continuous semimartingales with respect to fractional Brownian motion.

Original languageEnglish (US)
Pages (from-to)789-810
Number of pages22
JournalMathematics of Operations Research
Volume31
Issue number4
DOIs
StatePublished - Nov 1 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

Keywords

  • Fractional Brownian motion
  • Functional central limit theorem
  • Investor inertia
  • Market microstructure
  • Semi-Markov processes

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