Precise deviations for Cox processes with a shot noise intensity

Shot Noise Cox Processes

Generalised Shot Noise Cox Processes

We introduce a new class of Cox cluster processes called generalised shotnoise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process which drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be random. Thereby a very large class of models for aggregated or clustered point patterns is obtai...

Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity

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 Markov process theory. We apply the model to price stop-loss catastrophe reinsurance contract and catast...

Catastrophe Insurance Modelled with Shot-noise Processes

Shot-noise processes generalize compound Poisson processes in the following way: a jump (the shot) is followed by a decline (noise). This constitues a useful model for insurance claims in many circumstances: claims due to natural catastrophes or self-exciting processes exhibit similar features. We give a general account of shotnoise processes with time-inhomogeneous drivers and derive a number ...

Ruin Probabilities and Aggregrate Claims Distributions for Shot Noise Cox Processes

We consider a risk process Rt where the claim arrival process is a superposition of a homogeneous Poisson process and a Cox process with a Poisson shot noise intensity process, capturing the effect of sudden increases of the claim intensity due to external events. The distribution of the aggregate claim size is investigated under these assumptions. For both light-tailed and heavy-tailed claim s...