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: 1.68). 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:**In a very simple stock market, made by only two \emph{initially equivalent} traders, we discuss how the information can affect the performance of the traders. More in detail, we first consider how the portfolios of the traders evolve in time when the market is \emph{closed}. After that, we discuss two models in which an interaction with the outer world is allowed. We show that, in this case, the two traders behave differently, depending on \textbf{i)} the amount of information which they receive from outside; and \textbf{ii)}the quality of this information.Physica A: Statistical Mechanics and its Applications 02/2014; 404. · 1.68 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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