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

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<title>Potential measures for spectrally negative Markov additive processes with applications in ruin theory</title>
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<namePart>Feng, Runhuan</namePart>
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<abstract displayLabel="Summary">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.</abstract>
<note type="statement of responsibility">Runhuan Feng,  Yasutaka Shimizu</note>
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<title>Insurance : mathematics and economics</title>
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<publisher>Oxford : Elsevier, 1990-</publisher>
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<identifier type="issn">0167-6687</identifier>
<identifier type="local">MAP20077100574</identifier>
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<text>03/11/2014 Volumen 59 Número 1 - noviembre 2014 </text>
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