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...

In this paper, we study the Parisian time of a reflected Brownian motion with drift on a finite collection of rays. We derive the Laplace transform of the Parisian time using a recursive method, and provide an exact simulation algorithm to sample from the distribution of the Parisian time. The...

In this paper, we study a bivariate shot noise Hawkes process. This process includes both externally excited joint jumps following a homogeneous Poisson process and two separate self-excited jumps, which are two Poisson cluster processes. A constant rate of exponential decay is included in this...