Gibbs measure and Markov chain modeling for stock markets
We reviewed the recent work on Gibbs measure (statistical physics model) describing the collective price jumps in stock markets. We started with the study of a multivariate Markov chain model as a. stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes were coded into the sequences of up and down spins according to their signs. As the stationary state of the Markov chain, Gibbs measure was naturally derived, which formally coincides with spin glass model of disordered magnetic systems. The linear response of the system to external fields was examined to prove the fluctuation response theorem, Finally, the analysis of actual portfolios based on this model was briefly summarized.
KeywordsMarkov Chain Stock Market Stock Issue Price Change Spin Glass
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