In this paper we generalise the risk models beyond the ordinary framework of affine processes or Markov processes and study a risk process where the claim arrivals are driven by a Cox process with renewal shot-noise intensity. The upper bounds of the finite-horizon and infinite-horizon ruin...

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 propose a continuous-time stochastic intensity model, namely, two-phase dynamic contagion process(2P-DCP),for modelling the epidemic contagion of COVID-19 and investigating the lockdown effect based on the dynamic contagion model introduced by Dassios and Zhao (2011). It allows...

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...

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...

We introduce a numerically efficient simulation algorithm for Hawkes process with exponentially decaying intensity, a special case of general Hawkes process that is most widely implemented in practice. This computational method is able to exactly generate the point process and intensity process,...

In this paper, we introduce a new large family of Lévy-driven point processes with (and without) contagion, by generalising the classical self-exciting Hawkes process and doubly stochastic Poisson processes with non-Gaussian Lévy-driven Ornstein-Uhlenbeck type intensities. The resulting...

We consider a parsimonious framework of jump-diffusion models for price dynamics with stochastic price volatilities and stochastic jump intensities in continuous time. They account for conditional heteroscedasticity and also incorporate key features appearing in financial time series of price...

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...