Multivariate distributions with time and cross-dependence : aggregation and capital allocation

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<title>Multivariate distributions with time and cross-dependence</title>
<subTitle>: aggregation and capital allocation</subTitle>
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<namePart>Hu, Xiang</namePart>
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<namePart>Zhang, Lianzeng</namePart>
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<abstract displayLabel="Summary">This paper investigates risk aggregation and capital allocation problems for an insurance portfolio consisting of several lines of business. The class of multivariate INAR(1) processes is proposed to model different sources of dependence between the number of claims of the portfolio. The total capital required for the whole portfolio is evaluated under the TVaR risk measure, and the contribution of each line of business is derived under the TVaR-based allocation rule. We provide the risk aggregation and capital allocation formulas in the general case of continuous and strictly positive claim sizes and then in the case of mixed Erlang claim sizes. The impact of both time dependence and cross-dependence on the behavior of risk aggregation and capital allocation is numerically illustrated.

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<note type="statement of responsibility">Xiang Hu, Lianzeng Zhang</note>
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<topic>Dependencia</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080588953">
<topic>Análisis de riesgos</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080602437">
<topic>Matemática del seguro</topic>
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<classification authority="">6</classification>
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<title>Astin bulletin</title>
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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>
<identifier type="local">MAP20077000420</identifier>
<part>
<text>09/05/2022 Volumen 52 Número 2 - mayo 2022 , p. 669-706</text>
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