基于非广延统计力学观点的金融市场互动代理模型
An interacting-agent model of financial markets from the viewpoint of nonextensive statistical mechanics
摘要：
在本文中，我们提出了一个股票市场的互动代理模型。我们通过类伊辛模型来描述股票市场，以表达交易者受到其他交易者投资态度影响的趋势[1]，并将交易者的投资决策表达为非广延熵的最大熵原理。我们证明了交易者投资态度的均衡概率分布函数是{ \it q指数分布}。我们还表明，幂律分布的价格波动的波动性，这是经常在实证研究中证明，可以解释自然，我们的模型是基于许多相互作用的代理人的集体群体行为。
英文摘要：
In this paper we present an interacting-agent model of stock markets. We describe a stock market through an Ising-like model in order to formulate the tendency of traders getting to be influenced by the other traders' investment attitudes [1], and formulate the traders' decision-making regarding investment as the maximum entropy principle for nonextensive entropy. We demonstrate that the equilibrium probability distribution function of the traders' investment attitude is the {\it q-exponential distribution}. We also show that the power-law distribution of the volatility of price fluctuations, which is often demonstrated in empirical studies, can be explained naturally by our model which is based on the collective crowd behavior of many interacting agents.
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