A Limit Theorem for Financial Markets with Inert Investors

Erhan Bayraktar, Ulrich Horst and Ronnie Sircar

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.

Date: 2007-03
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Published in Mathematics of Operations Research, 2006, Volume 31 (4), 789-810

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:math/0703831

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