We introduce a new point process, the dynamic contagion process, by gener- alising the Hawkes process and the Cox process with shot noise intensity. Our process includes both self-excited and externally excited jumps, which could be used to model the dynamic contagion impact from endogenous and...

We introduce a new point process, the dynamic contagion process, by generalising the self excited Hawkes process (with exponential decay) by Hawkes (1971) and the Cox process with shot noise intensity by Dassios and Jang (2003). Our process includes both self excited and externally excited...

We introduce a bivariate Markov chain counting process with contagion for modelling the clustering arrival of loss claims with delayed settlement for an insurance company. It is a general continuous-time model framework that also has the potential to be applicable to modelling the clustering...

In this paper, we study a generalised CIR process with externally-exciting and self-exciting jumps, and focus on the distributional properties and applications of this process and its aggregated process. The aim of the paper is to introduce a more general process that includes many models in the...

We introduce a new point process, the dynamic contagion process, by generalizing the Hawkes process and the Cox process with shot noise intensity. Our process includes both self-excited and externally excited jumps, which could be used to model the dynamic contagion impact from endogenous and...

In this paper, we introduce a simple risk model with delayed claims, an extension of the classical Poisson model. The arrival of claims is assumed to be a Poisson process, claims follow a light-tailed distribution, and each loss payment of the claims will be settled with a random period of...

We introduce a new point process, the dynamic contagion process, by generalising the Hawkes process and the Cox process with shot noise intensity. Our process includes both self-excited and externally excited jumps, which could be used to model the dynamic contagion impact from endogenous and...

We introduce a bivariate Markov chain counting process with contagion for modelling the clustering arrival of loss claims with delayed settlement for an insurance company. It is a general continuous-time model framework that also has the potential to be applicable to modelling the clustering...