Naimzada Ahmad, Pireddu Marina
Department of Economics, Management and Statistics, University of Milano-Bicocca, U6 Building, Piazza dell'Ateneo Nuovo 1, 20126 Milano, Italy.
Department of Mathematics and Applications, University of Milano-Bicocca, U5 Building, Via Cozzi 55, 20125 Milano, Italy.
Chaos. 2015 Aug;25(8):083112. doi: 10.1063/1.4927831.
In the present paper, we consider a nonlinear financial market model in which, in order to decrease the complexity of the dynamics and to achieve price stabilization, we introduce a price variation limiter mechanism, which in each period bounds the price variation so that the current price is forced to belong to a certain interval determined by the price realization in the previous period. More precisely, we introduce such mechanism into a financial market model in which the price dynamics are described by a sigmoidal price adjustment mechanism characterized by the presence of two asymptotes that bound the price variation and thus the dynamics. We show that the presence of our asymptotes prevents divergence and negativity issues. Moreover, we prove that the basins of attraction are complicated only under suitable conditions on the parameters and that chaos arises just when the price limiters are loose enough. On the other hand, for some suitable parameter configurations, we detect multistability phenomena characterized by the presence of up to three coexisting attractors.
在本文中，我们考虑一个非线性金融市场模型，为了降低动态复杂性并实现价格稳定，我们引入了一种价格变化限制机制，该机制在每个时期限制价格变化，使得当前价格被迫属于由上一时期价格实现所确定的某个区间。更确切地说，我们将这种机制引入到一个金融市场模型中，在该模型中价格动态由一个具有两个渐近线的S形价格调整机制描述，这两个渐近线限制了价格变化从而也限制了动态。我们表明渐近线的存在防止了发散和负值问题。此外，我们证明吸引域仅在参数的合适条件下才复杂，并且只有当价格限制足够宽松时才会出现混沌。另一方面，对于一些合适的参数配置，我们检测到了以多达三个共存吸引子为特征的多重稳定性现象。
