标题： 二维动力系统稳定性分析及其在随机资产市场模型中的应用 显示英文标题

标题： Stability analysis with applications of a two-dimensional dynamical system arising from a stochastic model of an asset market

摘要： 我们分析了二维动力系统中平衡解的稳定性特性和轨道的周期性，该系统的轨道模拟了资产价格和对该资产的超额需求的变化过程。 该系统的构建基于一个针对单一风险资产市场的异质交互代理模型。 这种构建方法的一个优势是，得到的动力系统成为了一个宏观市场模型，它反映了通常仅在微观建模层面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) 交易者的投机趋势；(c) 市场参与者相对于资产基本面价值的个体评估的异质程度；以及 (d) 人口超额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可能原因。 在异质交互代理模型领域，使用动力系统来研究社会经济现象的随机模型的演化是很常见的。 然而，在文献中大部分情况下，这些动力系统是一维的。 我们的工作是该领域中少数构建并研究二维动力系统并将其用于解释社会经济现象的工作之一。 显示英文摘要

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.