Abstracts

In this project, we derive the diffusion approximation of the Bivariate Dynamic Contagion Processes (BDCP). The BDCP is a broad class of bivariate point processes including shot-noise Cox processes and Hawkes processes and it can be used in modelling high frequency events under the impact from both an external factor and an internal factor with contagion effects. We show that the BDCP converges weakly to a bivariate Ornstein-Uhlenbeck diffusion process based on the martingale central limit theorem. With the limiting diffusion system, we provide an approximation solution to filtering problems with point process observations. We apply the result on some problems in insurance.