The Paradox of Control in Banking Systems: Synchronisation of Marginally Binding Constraints, Correlated Responses and Dynamic Amplification

The systemic-risk literature extensively documents common exposures, constrained deleveraging, fire sales, contagion and macro-financial feedback effects. This paper proposes a more specific channel: systemic fragility may arise not from the homogeneity of prudential rules per se, but from the synchronisation of Kuhn-Tucker regimes in which particular constraints become simultaneously marginally binding. When a common shock activates similar constraints across banks, the associated Lagrange multipliers may converge, bringing their marginal optimisation conditions closer together and thereby increasing the conditional correlation of balance-sheet adjustments. The paper first develops this mechanism in a static framework and then examines its dynamic propagation through a transmission matrix incorporating memory, contagion and feedback effects. Dynamic fragility is interpreted not as necessary instability, but as an increase in the amplitude or persistence of shocks as the spectral radius of the transmission matrix approaches unity. A structural extension based on the Merton model subsequently outlines how the same mechanism may propagate to correlated default probabilities and joint default risk. Quantitative implementation of this extension, together with empirical testing of the proposed theoretical implications, is left for subsequent research.