Structural Stability of the Financial Market Model: Continuity of Superhedging Price and Model Approximation

The present paper continues the topic of our recent paper in the same journal, aiming to show the role of structural stability in financial modeling. In the context of financial market modeling, structural stability means that a specific “no-arbitrage” property is unaffected by small (with respect to the Pompeiu–Hausdorff metric) perturbations of the model’s dynamics. We formulate, based on our economic interpretation, a new requirement concerning “no arbitrage” properties, which we call the “uncertainty principle”. This principle in the case of no-trading constraints is equivalent to structural stability. We demonstrate that structural stability is essential for a correct model approximation (which is used in our numerical method for superhedging price computation). We also show that structural stability is important for the continuity of superhedging prices and discuss the sufficient conditions for this continuity.