## A limit theorem for financial markets with inert investors (2003)

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Venue: | Mathematics of Operations Research |

Citations: | 16 - 2 self |

### BibTeX

@ARTICLE{Bayraktar03alimit,

author = {Erhan Bayraktar and Ulrich Horst and Ronnie Sircar},

title = {A limit theorem for financial markets with inert investors},

journal = {Mathematics of Operations Research},

year = {2003},

pages = {33--54}

}

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### 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 modeling 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 ‘third parties’. 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.