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,...

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 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 consider a risk process with the arrival of claims modelled by a dynamic contagion process, a generalisation of the Cox process and Hawkes process introduced by Dassios and Zhao (2011). We derive results for the infinite horizon model that are generalisations of the...

This paper introduces a new model for portfolio credit risk incorporating default and spread widening in a simple and consistent framework. Credit spreads are modelled by geometric Brownian motions with a dependence structure powered by a t-copula. Their joint evolution drives the spreads...

Although the square-root process has long been used as an alternative to the Black-Scholes geometric Brownian motion model for option valuation, the pricing of Asian options on this diffusion model has never been studied analytically. However, the additivity property of the square-root process...

In this paper, we obtain the density function of the single barrier one-sided Parisian stopping time. The problem reduces to that of solving a Volterra integral equation of the first kind, where a recursive solution is consequently obtained. The advantage of this new method as compared to that...