In today's world of financial uncertainty, one major public concern is to assess (and possibly
improve) the stability of companies that take on risks. Actuaries have been aware of that …

This paper provides a new and accessible approach to establishing certain results
concerning the discounted penalty function. The direct approach consists of two steps. In the …

Externalities are the costs that a user of a common resource imposes on others. In the
context of an FCFS M/G/1 queue, where a customer with service demand x≥ 0 arrives when …

The classical compound Poisson risk model and the Sparre-Andersen risk model for
insurance businesses assume that the interclaim times and the claim amounts are …

Abstract We study the Gerber–Shiu functional of the classical risk process perturbed by a
spectrally negative α-stable motion. We provide representations of the scale functions of the …

A generalization of the Cramér–Lundberg risk model perturbed by a diffusion is proposed.
Aggregate claims of an insurer follow a compound Poisson process and premiums are …

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating
process and an investment return process. The investment return process is of standard a …

In this paper we consider Markov-modulated diffusion risk reserve processes. Using
diffusion approximation we show the relation to classical Markov-modulated risk reserve …

We study expected discounted penalty functionals for a class of Lévy processes having a
component given by the difference of two independent Poisson compound processes, and a …

The family of phase–type (PH) distributions has many useful properties such as closure
under convolution and mixtures, as well as rational Laplace transforms. PH distributions are …