In this paper, a particular class of matrix-exponential distributions is described, also with respect to its use in risk theory, namely phase-type distributions. Phase-type distributions have the important advantage of being suitable for approximating most of other distributions as well as being...

In this paper, we extend the work of Mitric and Sendova (2010), which considered the absolute ruin problem in a risk model with debit and credit interest, to renewal and non-renewal structures. Our first results apply to MAP processes, which we later restrict to the Sparre Andersen renewal risk...