  We construct a continuous time model for price-mediated contagion
precipitated by a common exogenous stress to the banking book of all firms in
the financial system. In this setting, firms are constrained so as to satisfy a
risk-weight based capital ratio requirement. We use this model to find
analytical bounds on the risk-weights for assets as a function of the market
liquidity. Under these appropriate risk-weights, we find existence and
uniqueness for the joint system of firm behavior and the asset prices. We
further consider an analytical bound on the firm liquidations, which allows us
to construct exact formulas for stress testing the financial system with
deterministic or random stresses. Numerical case studies are provided to
demonstrate various implications of this model and analytical bounds.
