In this paper we study the ruin problem for an insurance risk process driven by a spectrally-positive Markov additive process. Particular attention is given to the family of spectrally-positive Markov-modulated Lévy processes. We give an expression for the expected discounted penalty function by extending results available in the literature. In particular, we generalize some results in Biffis and Kyprianou (Insur Math Econ 46:85–91, 2010) to a more general setting provided by
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