Realistic Models of Financial Market and Structural Stability

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