This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs),
which constitute a rich class of point processes used extensively in stochastic modelling. Our …

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 …

In this paper, we consider a Markov additive insurance risk process under a randomized
dividend strategy in the spirit of Albrecher et al.(2011). Decisions on whether to pay …

In this paper, a risk model where claims arrive according to a Markovian arrival process
(MAP) is considered. A generalization of the well-known Gerber–Shiu function is proposed …

In this paper, we present a unified probabilistic approach to analyze a wide class of
insurance risk models in a ruin theoretical context. Contrary to the traditional analytic …

An insurance risk model where claims follow a Markovian arrival process (MArP) is
considered in this paper. It is shown that the expected present value of total operating costs …

We consider ruin problems for a risk model with a Markovian arrival process (MAP). In
particular, we study (1) the density of the time of ruin under two different assumptions on the …

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 …

In ruin theory, an insurer's income process is usually assumed to grow at a deterministic rate
of c> 0 over time. For instance, both the well-known Cramér–Lundberg risk process and the …

A MAP/PH risk model with possible by-claims and a dividend barrier is considered. Along
with the main claim, a by-claim also can occur with a certain probability but by-claims are …