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

Runhuan Feng, Yasutaka Shimizu

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)11-26
    Number of pages16
    JournalInsurance: Mathematics and Economics
    Volume59
    DOIs
    Publication statusPublished - 2014 Dec 1

    Fingerprint

    Ruin Theory
    Markov Additive Process
    Exit Problem
    Applied Probability
    Operator Matrix
    Explicit Solution
    Resolvent
    Closed-form Solution
    Fluctuations
    Differential equation
    Modeling
    Ruin theory

    Keywords

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

    ASJC Scopus subject areas

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

    Cite this

    Potential measures for spectrally negative Markov additive processes with applications in ruin theory. / Feng, Runhuan; Shimizu, Yasutaka.

    In: Insurance: Mathematics and Economics, Vol. 59, 01.12.2014, p. 11-26.

    Research output: Contribution to journalArticle

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