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...

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...

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...

In this paper, we study the excursion time of a Brownian motion with drift outside a corridor by using a four states semi-Markov model. In mathematical finance, these results have an important application in the valuation of double barrier Parisian options. In this paper, we obtain an explicit...

In this paper, we apply a single barrier strategy to optimise dividend payments in the situation where there is a time lag d0 between decision and implementation. Using a classical surplus process with exponentially distributed jumps, we obtain the optimal barrier b* which maximises the expected...

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...

This paper provides a survey of results on the quantiles of a Brownian motion with drift as well as a general Lévy process. The motivation is to calculate the price of related financial options. At the end of the paper some new results on variability orderings between various quantities...