Fitting Nonstationary Cox Processes : An application to fire insurance data

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<dc:creator>Albrecher, Hansjörg</dc:creator>
<dc:creator>Araujo-Acuna, José Carlos</dc:creator>
<dc:creator>Beirlant, Jan</dc:creator>
<dc:date>2021</dc:date>
<dc:description xml:lang="es">Sumario: 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.</dc:description>
<dc:identifier>https://documentacion.fundacionmapfre.org/documentacion/publico/es/bib/176731.do</dc:identifier>
<dc:language>spa</dc:language>
<dc:rights xml:lang="es">InC - http://rightsstatements.org/vocab/InC/1.0/</dc:rights>
<dc:subject xml:lang="es">Empresas de seguros</dc:subject>
<dc:subject xml:lang="es">Mercado de seguros</dc:subject>
<dc:subject xml:lang="es">Reclamaciones</dc:subject>
<dc:subject xml:lang="es">Seguro de incendio</dc:subject>
<dc:subject xml:lang="es">Cálculo actuarial</dc:subject>
<dc:type xml:lang="es">Artículos y capítulos</dc:type>
<dc:title xml:lang="es">Fitting Nonstationary Cox Processes : An application to fire insurance data</dc:title>
<dc:relation xml:lang="es">En: North American actuarial journal. - Schaumburg : Society of Actuaries, 1997- = ISSN 1092-0277. - 01/06/2021 Tomo 25 Número 2 - 2021 , p. 135-162</dc:relation>
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