Modeling discrete common-shock risks through matrix distributions

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<title>Modeling discrete common-shock risks through matrix distributions</title>
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<namePart>Bladt, Martin</namePart>
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<abstract displayLabel="Summary">This paper introduces a new class of bivariate Common-Shock Discrete Phase-Type (CDPH) distributions for modeling dependence in risk processes. The model couples two Markov chains that evolve jointly until a random common-shock time and then independently, yielding a tractable joint distribution. We derive key analytical properties, extend the framework to random-sum aggregate risks, and develop estimation procedures using the EM algorithm. Simulation studies and an application to bivariate insurance claim frequencies demonstrate the model's effectiveness, including its ability to estimate latent common-shock components</abstract>
<note type="statement of responsibility">Martin Bladt... [et al.]</note>
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<publisher>Belgium : ASTIN and AFIR Sections of the International Actuarial Association</publisher>
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<identifier type="issn">0515-0361</identifier>
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<text>19/01/2026 Volume 56 Issue 1 - January 2026 , p. 101 - 126</text>
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