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Realistic Models of Financial Market and Structural Stability

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  • Sergey N. Smirnov
  • Basil Papadopoulos

Abstract

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.

Suggested Citation

  • Sergey N. Smirnov & Basil Papadopoulos, 2021. "Realistic Models of Financial Market and Structural Stability," Journal of Mathematics, Hindawi, vol. 2021, pages 1-8, June.
    • Handle: RePEc:hin:jjmath:6651324
    DOI: 10.1155/2021/6651324
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