Abstract The Gerber-Shiu function provides a unified framework for the evaluation of a
variety of risk quantities. Ever since its establishment, it has attracted constantly increasing …

This paper defines a new class of fractional differential operators alongside a family of
random variables whose density functions solve fractional differential equations equipped …

The concept of integro-differential algebra has been introduced recently in the study of
boundary problems of differential equations. We generalize this concept to that of integro …

In this article, we provide the first systematic numerical study on, via the popular Fourier-
cosine (COS) method, finite-time Gerber--Shiu functions with the risk process being driven …

A level-dependent Lévy process solves the stochastic differential equation d U (t)= d X (t)− ϕ
(U (t)) dt, where X is a spectrally negative Lévy process. A special case is a multi-refracted …

This paper concerns an optimal dividend distribution problem for an insurance company
with surplus-dependent premium. In the absence of dividend payments, such a risk process …

The aim of this paper is to analyze a general class of storage processes, in which the rate at
which the storage level increases or decreases is assumed to be an affine function of the …

We provide a survey of so-called shot-noise queues: queueing models with the special
feature that the server speed is proportional to the amount of work it faces. Several results …

The Markov additive process (MAP) has become an increasingly popular modeling tool in
the applied probability literature. In many applications, quantities of interest are represented …

The main goal of this text is comprehensive study of time homogeneous Markov chains on
the real line whose drift tends to zero at infinity, we call such processes Markov chains with …