Article

# A quantum statistical approach to simplified stock markets

Dipartimento di Metodi e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I - 90128 Palermo, Italy

Physica A: Statistical Mechanics and its Applications (Impact Factor: 1.72). 10/2009; DOI: 10.1016/j.physa.2009.07.006 Source: RePEc

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**ABSTRACT:**We investigate the behavior of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is presumed to oscillate and damp in a quantum spatial-periodic harmonic oscillator potential well. Complicated non-linear relations including inter-band positive correlation and intra-band negative correlation between the volatility and the trading volume of stocks are derived by considering the energy band structure of the model. The validity of price limitation is then examined and abnormal phenomena of a price-limited stock market (Shanghai Stock Exchange) of China are studied by applying our quantum model.05/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper shows that Hamiltonians and operators can also be put to good use even in contexts which are not purely physics based. Consider the world of finance. The work presented here {models a two traders system with information exchange with the help of four fundamental operators: cash and share operators; a portfolio operator and an operator reflecting the loss of information. An information Hamiltonian is considered and an additional Hamiltonian is presented which reflects the dynamics of selling/buying shares between traders. An important result of the paper is that when the information Hamiltonian is zero, portfolio operators commute with the Hamiltonian and this suggests that the dynamics are really due to the information. Under the assumption that the interaction and information terms in the Hamiltonian have similar strength, a perturbation scheme is considered on the interaction parameter. Contrary to intuition, the paper shows that up to a second order in the interaction parameter, a key factor in the computation of the portfolios of traders will be the initial values of the loss of information (rather than the initial conditions on the cash and shares). Finally, the paper shows that a natural outcome from the inequality of the variation of the portfolio of trader one versus the variation of the portfolio of trader two, begs for the introduction of `good' and `bad' information. It is shown that `good' information is related to the reservoirs (where an infinite set of bosonic operators are used) which model rumors/news and external facts, whilst `bad' information is associated with a set of two modes bosonic operators.Physica Scripta 12/2014; 90(1). · 1.30 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We investigate the relevance between quantum open systems and stock markets. A Quantum Brownian motion model is proposed for studying the interaction between the Brownian system and the reservoir, i.e., the stock index and the entire stock market. Based on the model, we investigate the Shanghai Stock Exchange of China from perspective of quantum statistics, and thereby examine the behaviors of the stock index violating the efficient market hypothesis, such as fat-tail phenomena and non-Markovian features. Our interdisciplinary works thus help to discovery the underlying quantum characteristics of stock markets and develop new research fields of econophysics.04/2014;

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