We study the price dynamics generated by a stochastic version of a Day–Huang type asset market model with heterogenous, interacting market participants. To facilitate the analysis, we introduce a methodology that allows us to assess the consequences of changes in uncertainty on the dynamics of an asset price process close to stable equilibria. In particular, we focus on noise-induced transitions between bull and bear states of the market under additive as well as parametric noise. Our results are obtained by combining the stochastic sensitivity function (SSF) approach, a mixture of analytical and numerical techniques, due to Mil’shtein and Ryashko (1995) with concepts and techniques from the study of non-smooth 1D maps. We find that the stochastic sensitivity of the respective bull and bear equilibria in the presence of additive noise is higher than under parametric noise. Thus, recurrent transitions are likely to be observed already for relatively low intensities of additive noise.

我们研究由Day-Huang型资产市场模型的随机版本与异类，相互作用的市场参与者所产生的价格动态。为便于分析，我们引入了一种方法，使我们能够评估不确定性变化对接近稳定均衡的资产价格过程动态的影响。特别是，我们关注于在加性以及参数性噪声下，噪声引起的市场牛市与熊市之间的过渡。我们的结果是通过将随机敏感度函数（SSF）方法，分析和数值技术的混合（由于Mil'shtein和Ryashko（1995））与非光滑一维地图研究的概念和技术相结合而获得的。我们发现，在存在加性噪声的情况下，各个牛市和熊市均衡的随机敏感性高于在参数性噪声下的敏感性。因此，对于附加噪声相对较低的强度，很可能已经观察到循环过渡。