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

首先，我们建立了考虑交叉持股、违约成本和债券优先级的公司债券定价模型。我们提出了一个早期清算支付向量，以捕捉金融危机。我们证明了它们的存在性和导出它们的方法。其次，我们引入了一个最优资本注入问题，并给出了求解该问题的算法，该问题可以用Eisenberg和Noe模型下的线性规划形式表示。我们提出了一个顺序的方法来解决公司的支付给债务持有人和政府的资本注入到公司。我们可以证明，资本注入的优先规则并不取决于政府的预算数额。

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.