连续双向拍卖多代理模型中的投资者情绪
Investor's sentiment in multi-agent model of the continuous double auction
摘要：
我们引入并严格对待一个新的多代理模型的连续双向拍卖或换句话说，订单簿（OB）。它旨在解释当影响市场的新信息到达时市场的集体行为。该模型的新特征是两个额外的缓慢变化的参数，即所谓的情感函数。这些情绪函数衡量两组投资者的公平价格概念，即多头和空头。我们的模型指定的情感函数的时间演化微分方程，并构成一个非线性马尔可夫过程，表现出长期的相关性。我们解释了情绪函数方程背后的直觉，并提出了数值模拟，这表明我们的模型的行为是类似于真实市场的行为。我们还得到了模型的扩散极限，变波动率的Ornstein-Uhlenbeck型过程。波动性与多头和空头对证券公平价格的不同意见成正比。本文是补充我们以前的工作，数学证明。
英文摘要：
We introduce and treat rigorously a new multi-agent model of the continuous double auction or in other words the order book (OB). It is designed to explain collective behaviour of the market when new information affecting the market arrives. The novel feature of the model is two additional slow changing parameters, the so-called sentiment functions. These sentiment functions measure the conception of the fair price of two groups of investors, namely, bulls and bears. Our model specifies differential equations for the time evolution of sentiment functions and constitutes a nonlinear Markov process which exhibits long term correlations. We explain the intuition behind equations for sentiment functions and present numerical simulations which show that the behaviour of our model is similar to the behaviour of the real market. We also obtain a diffusion limit of the model, the Ornstein-Uhlenbeck type process with variable volatility. The volatility is proportional to the difference of opinions of bulls and bears about the fair price of a security. The paper is complimentary to our previous work where mathematical proofs are presented.
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