A Markov additive risk process with a dividend barrier

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We study a risk process with dividend barrier b where the claims arrive according to a Markovian additive process (MAP). For spectrally negative MAPs, we present linear equations for the expected discounted dividends and the expected discounted penalty function. We apply results for the first exit times of spectrally negative Lévy processes and change-of-measure techniques. Explicit expressions are given when there are positive and negative claims, with phase-type distribution.

Original languageEnglish
Pages (from-to)451-489
Number of pages39
JournalAdvances in Applied Probability
Issue number2
StatePublished - Jun 2013


  • Exit time
  • Markov arrival process
  • Phase-type distribution
  • Reflected process
  • Spectrally negative Lévy process

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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