Leitura do Dia - A Limit Theorem for Financial Markets with Inert Investors

A Limit Theorem for Financial Markets with Inert Investors
Erhan Bayraktar
Ulrich Horst
Ronnie Sircar

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.

Certamente um dos artigos mais importantes para as minhas pesquisas. Ele justifica vários resultados e procedimentos que eu venho trabalhando, e levanta vários pontos de pesquisa. Microestrutura de mercado, dependência longa, fractional brownian motion ...