Fitting Nonstationary Cox Processes : An application to fire insurance data

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<title>Fitting Nonstationary Cox Processes</title>
<subTitle>: An application to fire insurance data</subTitle>
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<namePart>Araujo-Acuna, José Carlos</namePart>
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<namePart>Beirlant, Jan</namePart>
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<abstract displayLabel="Summary">In insurance practice, claims often occur in clusters and their arrivals may depend on various external and time-dependent factors. In this article, we propose a statistical approach for modeling claim arrivals by considering clustered arrivals and non-stationarity simultaneously. To this end, we extend the Cox process methodology with Lévy subordinators presented in Selch and Scherer (2018) relaxing the stationarity of increments assumption. A particular special case of the proposed approach is a dynamic and flexible model of negative binomially distributed claim numbers with trends and seasonal variations of the parameters. For illustration purposes, we fit the model to a fire insurance portfolio and show that it allows the modeling of cluster occurrences in a seasonal pattern while preserving overdispersion, which is frequently observed in claim count data. We illustrate its use in forecasting and Value-at-Risk and expected shortfall computations of the aggregate insurance risk. Finally, we provide a multivariate extension of the model, where simultaneous cluster arrivals in different components are generated by a nonstationary common subordinator.</abstract>
<note type="statement of responsibility">Hansjorg Albrecher, José Carlos Araujo-Acuna, Jan Beirlant</note>
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<topic>Empresas de seguros</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080586294">
<topic>Mercado de seguros</topic>
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<topic>Reclamaciones</topic>
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<topic>Seguro de incendio</topic>
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<topic>Cálculo actuarial</topic>
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<title>North American actuarial journal</title>
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<publisher>Schaumburg : Society of Actuaries, 1997-</publisher>
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<identifier type="issn">1092-0277</identifier>
<identifier type="local">MAP20077000239</identifier>
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<text>01/06/2021 Tomo 25 Número 2 - 2021 , p. 135-162</text>
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