This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another...

The simulation of risk processes is a standard procedure for insurance companies. The generation of simulated (aggregated) claims is vital for the calculation of the amount of loss that may occur. Simulation of risk processes also appears naturally in rating triggered step-up bonds, where the...

We consider the subject of approximating tail probabilities in the general compound renewal process framework, where severity data are assumed to follow a heavy-tailed law (in that only the first moment is assumed to exist). By using weak convergence of compound renewal processes to Lévy...

In this article, we build on Chernobai et al. [1]'s procedure for modelling left-truncated data via a compound non-homogeneous Poisson process. The contribution we make is that we modify the fitting process introduced so that it is systematically applicable in the context of data that is not...

In this paper, we consider a two-dimensional risk process in which the companies split each claim and premium in a fixed proportion. It serves as a classical framework of a quota-share reinsurance contract for a given business line. Such a contract reduces the insurer's exposure to the...

We introduce here a diffusion-type approximation of the ruin probability both in finite and infinite time for a two-dimensional risk process, where claims and premiums are shared with a predetermined proportion. This type of process is often called the insurer-reinsurer model. We assume that the...