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...

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 the weak convergence of compound renewal processes to a-stable...

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...

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...

A user friendly approach to modeling the risk process is presented. It utilizes the insurance library of the XploRe computing environment which is accompanied by on-line, hyperlinked and freely downloadable from the web manuals and e-books. The empirical analysis for Danish fire losses for the...