Cavalli F, Naimzada A, Pecora N
Department of Mathematical Sciences, Mathematical Finance and Econometrics, Catholic University, Via Necchi 9, 20123 Milano, Italy.
Department of Economics, Management and Statistics, University of Milano-Bicocca, U6 Building, Piazza dell'Ateneo Nuovo 1, 20126 Milano, Italy.
Chaos. 2017 Oct;27(10):103120. doi: 10.1063/1.4994617.
In the present paper, we investigate the dynamics of a model in which the real part of the economy, described within a multiplier-accelerator framework, interacts with a financial market with heterogeneous speculators, in order to study the channels through which the two sectors influence each other. Employing analytical and numerical tools, we investigate stability conditions as well as bifurcations and possible periodic, quasi-periodic, and chaotic dynamics, enlightening how the degree of market interaction, together with the accelerator parameter and the intervention of the fiscal authority, may affect the business cycle and the course of the financial market. In particular, we show that even if the steady state is locally stable, multistability phenomena can occur, with several and complex dynamic structures coexisting with the steady state. Finally, simulations reveal that the proposed model is able to explain several statistical properties and stylized facts observed in real financial markets, including persistent high volatility, fat-tailed return distributions, volatility clustering, and positive autocorrelation of absolute returns.
在本文中，我们研究了一个模型的动态特性，其中经济的实际部分在乘数 - 加速数框架内进行描述，并与具有异质投机者的金融市场相互作用，目的是研究这两个部门相互影响的渠道。我们运用分析和数值工具，研究稳定性条件以及分岔现象，还有可能出现的周期性、准周期性和混沌动态，阐明市场相互作用程度、加速数参数以及财政当局的干预如何影响商业周期和金融市场的走势。特别地，我们表明即使稳态是局部稳定的，也可能出现多重稳定性现象，即几种复杂的动态结构与稳态共存。最后，模拟结果表明所提出的模型能够解释在实际金融市场中观察到的几种统计特性和典型事实，包括持续的高波动性、厚尾收益分布、波动聚集以及绝对收益的正自相关性。
