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We construct a continuous time model for price-mediated contagionprecipitated by a common exogenous stress to the banking book of all firms inthe financial system. In this setting, firms are constrained so as to satisfy arisk-weight based capital ratio requirement. We use this model to findanalytical bounds on the risk-weights for assets as a function of the marketliquidity. Under these appropriate risk-weights, we find existence anduniqueness for the joint system of firm behavior and the asset prices. Wefurther consider an analytical bound on the firm liquidations, which allows usto construct exact formulas for stress testing the financial system withdeterministic or random stresses. Numerical case studies are provided todemonstrate various implications of this model and analytical bounds.

Capital Regulation under Price Impacts and Dynamic Financial Contagion