在现代金融系统中，人们逐渐开始关注整个银行业的系统性风险而不仅仅是个体风险，而传统经济学中个体银行投资组合多元化理论对于系统性风险来说并不一定是有效的，因此对于银行投资组合多元化与系统性风险之间的关系仍需要深入研究。本文基于简化的金融市场，通过资产负债表刻画银行和资产之间的联系，构建了描述银行破产边界的数学模型，并以此为基础分别研究了银行个体风险、系统性风险、考虑拆借关系的系统性风险以及同时考虑减价出售和拆借关系的系统性风险之间的区别与联系，进而分析了银行投资组合多元化对不同风险的影响。最后，参考实际金融市场中的参数取值，对本文构建的模型进行了数值实验，研究结果表明：多元化会使银行的投资组合变得相似从而更容易引发系统性风险，资产减价出售和银行间拆借关系的存在同样会增加银行系统性风险，因而通过减少投资组合多元化和控制银行拆借比例等措施可以在一定程度上降低系统性风险的发生，这对于系统性风险的监管具有较高的参考价值。
It has been widely believed that the overall systemic risk instead of the individual risk should be paid more attention in the modern financial system. Meanwhile, the investment portfolios diversification theory which benefits the individual bank in traditional economics is no longer desirable as a result of the systemic risk. Therefore, the relationship between investment portfolios diversification of banks and the systemic risk still needs a further study. In a simplified financial market, the balance sheet is used to describe the connection between banks and assets, then a mathematical model is set up to depict the bankruptcy boundary of banks. The difference and relationship among individual risk, systematic risk, systemic risk with interbank loans, systemic risk with both fire sale and interbank loans are respectively studied based on the mathematical model. Finally, the mathematical model is numerical tested according to actual parameter values in the financial market and the results show that, investment portfolios of different banks will become similar with each other because of diversification which incurs the systemic risk more easily. The existence of fire sale and interbank loans will also increase the systemic risk. Therefore, the systemic risk can be controlled to a certain extent by reducing investment portfolio diversification and interbank loans ratio and this result provides a high reference value for the supervision of systemic risk.
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