股市中危机传播的SIR模型及其仿真

Susceptible-infected-removed (SIR) model of crisis spreading in the correlated network of listed companies and their main stock-holders

选择上市公司的大股东信息,建立了上市公司及其大股东间的持股关联网络.考虑到上市公司与股东间因为资金流减小或资金链断裂而相互影响所导致的危机在网络中的传播行为,推导出股市中危机传播的SIR模型的计算方法.继而对网络出现随机故障和遇到蓄意攻击时,危机在网络中的传播过程进行仿真分析.研究表明:当网络中的大型上市公司或控股集团(Hub节点)被蓄意攻击或出现故障时,危机在网络中传播速度极快,造成的破坏力很大,网络表现出明显的脆弱性,从而容易产生多米诺骨牌效应.该方法为未来对经济危机的传播机理的深入研究提供了一个可供借鉴的方法.

According to the annual reports of listed companies, a correlated network of the listed companies and their main stock holders are established. Taking into account the mutual influences, resulted from reduced cash flows or the fracture of capital chain, between the listed companies and the main stock holders, a suscep- tible-infected-removed model of crisis spreading （SIR） in the stock markets is established. Then, a numerical computation is used to analyze the crisis spreading in the correlated networks when the networks meet the random failure or the intentional attacks. If there are some failures or attacks on the large-scale listed companies or large-scale holding companies （Hub vertices） in the networks, the crisis will spread in a high speed and cause catastrophic damages. In this condition, the networks show a obvious vulnerability; and the stock markets may show domino effects. The research approaches in this paper are helpful for further researches on the transmission mechanism of the economic crisis.