 Potential measures for spectrally negative Markov additive processes with applications in ruin theoryRunhuan Feng and Yasutaka Shimizu Insurance: Mathematics and Economics, 2014, vol. 59, issue C, 11-26 Abstract: 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. Keywords: Markov additive processes; Potential measure; Resolvent density; Markov renewal equation; Scale matrix; Exit problems (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:59:y:2014:i:c:p:11-26 DOI: 10.1016/j.insmatheco.2014.08.001 Access Statistics for this article Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu More articles in Insurance: Mathematics and Economics from Elsevier |
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