Quantum Brownian motion model for the stock market
arXiv:1405.3512 · doi:10.1016/j.physa.2016.02.026
Abstract
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system--a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.
References in corpus (8)
- Fundamental Aspects of Quantum Brownian Motion
- Multifractal analysis of Chinese stock volatilities based on partition function approach
- Multifractality in stock indexes: Fact or fiction?
- A quantum model for the stock market
- A finite-dimensional quantum model for the stock market
- Quantum spatial-periodic harmonic model for daily price-limited stock markets
- Thermodynamics of inequalities: from precariousness to economic stratification
- Non-Markovian Caldeira--Leggett quantum master equation
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- Stationarity of the detrended price return in stock markets
- On non-commutativity in quantum theory (I): from classical to quantum probability
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