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...

In this paper, we study a generalised CIR process with externally-exciting and self-exciting jumps, and focus on the distributional properties and applications of this process and its aggregated process. The aim of the paper is to introduce a more general process that includes many models in the...

In this paper, we study a generalised CIR process with externally-exciting and self-exciting jumps, and focus on the distributional properties and applications of this process and its aggregated process. The aim of the paper is to introduce a more general process that includes many models in the...

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...

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 a bivariate shot noise self-exciting process. This process includes both externally excited joint jumps, which are distributed according to a shot noise Cox process, and two separate self-excited jumps, which are distributed according to the branching structure of a...

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...