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A Limit Theorem for Financial Markets with Inert Investors

Please always quote using this URN:urn:nbn:de:0296-matheon-857
  • 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.

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Metadaten
Author:Erhan Bayraktar, Ulrich Horst, Ronnie Sircar
URN:urn:nbn:de:0296-matheon-857
Referee:Hans Föllmer
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2004/02/13
Release Date:2004/02/13
Institute:Humboldt-Universität zu Berlin
Technische Universität Berlin
Preprint Number:76
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