A Limit Theorem for Financial Markets with Inert Investors
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.
Keywords
Cite
@article{arxiv.math/0703831,
title = {A Limit Theorem for Financial Markets with Inert Investors},
author = {Erhan Bayraktar and Ulrich Horst and Ronnie Sircar},
journal= {arXiv preprint arXiv:math/0703831},
year = {2008}
}