Modeling and simulation of the market fluctuations by the finite range contact systems

Effect of boundary conditions on stochastic Ising-like financial market price model

“…If ξ t (x) | N (x(t)) |> 0, there are more buyers than sellers, then the stock price is auctioned up, similarly for other cases. From the above definitions and [2,4,5], we define the stock price of the model at time t(t = 1, 2,...)as S t = e γ ξ t (x)|N (x(t))|/n 2 S t−1 , where ¿ > 0 is the depth parameter of the market, and S 0 be the the initial price at time t = 0. Then, we have…”

“…As the stock markets are becoming deregulated worldwide, the modeling of the dynamics of the forward prices is becoming a key problem in risk management, physical assets valuation and derivatives pricing, see [1][2][3][4][5][6], and it is also important to understand the statistical properties of fluctuations of stock price in globalized securities markets, for example see [7,8]. A complex behavior can emerge due to the interactions among smallest components of that system, see [9], and it is often a successful strategy to analyze the behavior of a complex system by studying these components.…”

“…In financial markets, these components are comprised by the market participants who buy and sell assets in order to realize their trading and investment decisions. Similar to physical systems, the superimposed flow of all individual orders submitted to the exchange trading system initiated by market participants and its change in time generate a complex system with fascinating properties, see [1,2].…”

“…Recently, the theory of stochastic interacting particle systems [10][11][12] has been applied to investigate the statistical behaviors of fluctuations for stock prices, and the corresponding valuation and hedging of contingent claims for these price process models are also studied, see [1,2,11,12]. In the present article, we suppose that traders determine their positions at each time by observing the market information (and then evaluating the market behavior, market sentiment and their trading strategies), each trader is thought to be a subunit in the stock market, and may take positive (buying) position, negative (selling) position or neutral position, denoted by +, -, and 0, respectively.…”

Complex System Analysis on Voter Stochastic System and Jump Time Effective Neural Network of Stock Market

“…By applying the theory of stochastic systems, some research work has been done to investigate the statistical behaviors of fluctuations for stock markets, and the corresponding valuation and hedging of contingent claims for the price process models are also studied [1][2][3][4][5][6][7] . In these financial models, the main assumption is that the stock price fluctuation is influenced by the information in a stock market, and the investors decide their investment opinions by other investors' attitudes, so the investors' investment attitudes to the stock market lead to the stock price fluctuation.…”