Potential measures for spectrally negative Markov additive processes with applications in ruin theory

Runhuan Feng, Yasutaka Shimizu

Research output: Contribution to journalArticle

9 Citations (Scopus)


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 as functionals of MAPs and potential measures, also known as resolvent measures, have played a key role in the representations of explicit solutions to these functionals. In this paper, closed-form solutions to potential measures for spectrally negative MAPs are found using a novel approach based on algebraic operations of matrix operators. This approach also provides a connection between results from fluctuation theoretic techniques and those from classical differential equation techniques. In the end, the paper presents a number of applications to ruin-related quantities as well as verification of known results concerning exit problems.

Original languageEnglish
Pages (from-to)11-26
Number of pages16
JournalInsurance: Mathematics and Economics
Publication statusPublished - 2014 Dec 1



  • Exit problems
  • Markov additive processes
  • Markov renewal equation
  • Potential measure
  • Resolvent density
  • Scale matrix

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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