Complex Dynamics of Credit Risk Contagion with Time-Delay and Correlated Noises

The stochastic time-delayed system of credit risk contagion driven by correlated Gaussian whitenoises is investigated. Novikov’s theorem, the time-delay approximation, the path-integral approach, and first-orderperturbation theory are used to derive time-delayed Fokker-Planck model and the stationary probability distributionfunction of the dynamical system of credit risk contagion in the financial market. Using the method of numericalsimulation, the Hopf bifurcation and chaotic behaviors of credit risk contagion are analyzed when time-delay andnonlinear resistance coefficient are varied and the effects of time-delay, nonlinear resistance and the intensity andthe correlated degree of correlated Gaussian white noises on the stationary probability distribution of credit riskcontagion are investigated. It is found that, as the infectious scale of credit risk and the wavy frequency of creditrisk contagion are increased, the stability of the system of credit risk contagion is reduced, the dynamical system ofcredit risk contagion gives rise to chaotic phenomena, and the chaotic area increases gradually with the increase intime-delay. The nonlinear resistance only influences the infectious scale and range of credit risk, which is reducedwhen the nonlinear resistance coefficient increases. In addition, the curve of the stationary probability distribution ismonotone decreasing with the increase in parameters value of time-delay, nonlinear resistance, and the intensity andthe correlated degree of correlated Gaussian white noises.