The main aim of this article is to show the role of structural stability in financial modelling; that is, a specific “no-arbitrage” property is unaffected by small perturbations of the model’s dynamics. We prove that under the structural stability assumption, given a convex compact-valued multifunction, there exists a stochastic transition kernel with supports coinciding with this multifunction and one that is strong Feller in the strict sense. We also demonstrate preservation of structural stability for sufficiently small deviations of transition kernels for different probability metrics.

中文翻译：

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金融市场和结构稳定性的现实模型

本文的主要目的是展示结构稳定性在金融建模中的作用；也就是说，特定的“无套利”属性不受模型动态的微小扰动的影响。我们证明，在结构稳定性假设下，给定一个凸紧值多功能函数，存在一个随机过渡核，其支持与该多功能重合，并且是严格意义上的强 Feller。我们还展示了对于不同概率度量的转换内核的足够小的偏差保持结构稳定性。