An unified evaluation model for the financial systemic risk under financial crisis

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First, we presented the pricing model of the corporate securities with cross-holdings, default costs and bond seniorities. We propose an early clearing payment vector to capture the financial crisis. We showed the existence of them and the method to derive them. Second, we introduced an optimal capital injection problem and proposed an algorithm to solve it. The problem can be represented by a linear programming formulation under Eisenberg and Noe's model. We presented a sequential method to solve both the firm's payoff to debt holders and the government's capital injection to the firms. We can show that the priority rule of capital injection does not depend on the amount of the budget by the government.