A Limit Theorem for Financial Markets with Inert Investors
Mathematics of Operations Research, 2006, Volume 31 (4), 789-810.
25 Pages Posted: 30 May 2016
Date Written: December 1, 2004
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.
Keywords: Semi-Markov processes; fractional Brownian motion; functional central limit theorem; market microstructure; investor inertia.
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