| Stochastic process models are one of the important areas of mathematical research.Because stochastic processes have important characteristics such as equivalence and independence,they are accurate for constructing financial default risk models and reduce the strength parameter indicators that characterize the macro stability of financial markets at extreme values.And the error under incomplete data has a significant effect.At the same time,the attenuation factor of the cumulative number of defaults is added to the contagion factor of the general strength default parameter model,which reduces the over-sensitive characteristics of the model and improves the model's stability and anti-interference ability,which makes the model face the extreme values or the thick-tailed distribution The measurement of the average default arrival rate under the conditions also performs well.At the same time,due to the existence of some observable explanatory variables and the point process path in the process of the point process generated by incomplete data,the likelihood function of the point process intensity parameter model caused the filtering problem.This paper uses the filter likelihood method to solve the filtering problem in the strength parameter model parameter estimation.At the same time,this paper uses China's financial default data from March 2014 to May 2019 to compare and analyze the optimized CM model and the ERM model that add the cumulative default frequency attenuation effect to HAWKES self-excitation infection items.Pros and cons of the degree of fitting of China's financial default data in a small sample.The results show that the Optimized CM model has a better effect on the fitting of financial default data in China because of the Cluster default effect.At the same time,the filtering likelihood method has a better performance on the parameter estimation of the model in terms of parameter estimation efficiency,convergence speed and estimation accuracy. |
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