Systemic Runs and the Dimension of Financial Fragility
Abstract
Financial institutions meet withdrawals by selling overlapping portfolios, so creditor runs and market prices are jointly determined. I derive an exact asset-market representation. A local architecture rank bounds propagation dimensions for queries that factor through bank-cushion shocks and withdrawal outcomes. One-mode alignment delivers a global scalar representation, while one dominant mode emerges near local spectral instability. A date-0 maturity measure supplies liabilities across cumulative stress windows. Liquidity, depth, and recovery jointly determine local amplification and a hump-shaped uniqueness envelope. Runnable maturity and common-asset exposure can be locally excessive in an ex ante balance-sheet game. State-contingent regulatory wedges incorporate every feedback round. Their expectations govern unconditional date-0 charges. The Jacobian rank of the state-contingent wedge map gives the minimum local regulatory-state dimension. The feedback-mediated propagation dimension of those wedges is bounded by the architecture rank. Left-right centralities rank equal-cost stability interventions.