Showing 1 - 10 of 14
Applying piecewise deterministic Markov processes theory, the probability generating function of a Cox process, incorporating with shot noise process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise process at claim jump times, using...
Persistent link: https://www.econbiz.de/10010745484
We use the Cox process (or a doubly stochastic Poisson process) to model the claim arrival process for catastrophic events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic...
Persistent link: https://www.econbiz.de/10010745717
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...
Persistent link: https://www.econbiz.de/10011125907
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,...
Persistent link: https://www.econbiz.de/10011126347
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...
Persistent link: https://www.econbiz.de/10011126559
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...
Persistent link: https://www.econbiz.de/10010884699
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...
Persistent link: https://www.econbiz.de/10010744808
In this paper, we apply the single barrier strategy to optimize the dividend payment in the situation where there is a time lag d 0 between decision and implementation. Using a Brownian motion with drift as the surplus process, we obtain the optimal barrier b* which maximises the expected...
Persistent link: https://www.econbiz.de/10010745176
In this paper, we extend the concept of ruin in risk theory to the Parisian type of ruin. For this to occur, the surplus process must fall below zero and stay negative for a continuous time interval of specified length. Working with a classical surplus process with exponential jump size, we...
Persistent link: https://www.econbiz.de/10010745397
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...
Persistent link: https://www.econbiz.de/10010745594