摘要翻译：
本文分析了一类二维动力系统平衡解的稳定性和轨道的周期性，该系统的轨道模拟了资产价格的演化和对该资产的超额需求。该系统的构建基于一个单一风险资产市场的异构交互代理模型。这种构建过程的一个优点是，由此产生的动力系统成为一个宏观市场模型，它反映了通常只在微观建模水平上考虑的市场数量和质量。系统的参数对应于：(a)市场中投机者的比例；(b)交易商的投机趋势；(c)市场代理人对资产基本价值的特殊评估的异质性程度；人口过剩需求对资产价格更新增量的反馈强度。这种对应关系使我们能够利用我们的结果来推断真实资产市场中价格和需求波动出现的合理原因。利用动力系统研究社会经济现象的随机模型的演化是异构交互agent模型领域中的一个非常普遍的研究方法。然而，在文献中出现的绝大多数情况下，这些动力系统都是一维的。我们的工作是少数几个在该领域建立和研究二维动力系统，并应用它们来解释社会经济现象。
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英文标题：
《Stability analysis with applications of a two-dimensional dynamical
  system arising from a stochastic model of an asset market》
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作者：
Vladimir Belitsky, Antonio L. Pereira, Fernando P. de Almeida Prado
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Dynamical Systems        动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
  We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system's parameters correspond to: (a) the proportion of speculators in a market; (b) the traders' speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset's fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market.   The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study two-dimensional dynamical systems and apply them for explanation of socio-economic phenomena.
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PDF链接：
https://arxiv.org/pdf/0909.4815