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Fitting Nonstationary Cox Processes : An application to fire insurance data

Recurso electrónico / Electronic resource
Registro MARC
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100  ‎$0‎MAPA20080650025‎$a‎Albrecher, Hansjörg
24510‎$a‎Fitting Nonstationary Cox Processes‎$b‎: An application to fire insurance data‎$c‎Hansjorg Albrecher, José Carlos Araujo-Acuna, Jan Beirlant
520  ‎$a‎In 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.
650 4‎$0‎MAPA20080590567‎$a‎Empresas de seguros
650 4‎$0‎MAPA20080586294‎$a‎Mercado de seguros
650 4‎$0‎MAPA20080567118‎$a‎Reclamaciones
650 4‎$0‎MAPA20080587871‎$a‎Seguro de incendio
650 4‎$0‎MAPA20080579258‎$a‎Cálculo actuarial
7001 ‎$0‎MAPA20210030079‎$a‎Araujo-Acuna, José Carlos
7001 ‎$0‎MAPA20110007928‎$a‎Beirlant, Jan
7730 ‎$w‎MAP20077000239‎$t‎North American actuarial journal‎$d‎Schaumburg : Society of Actuaries, 1997-‎$x‎1092-0277‎$g‎01/06/2021 Tomo 25 Número 2 - 2021 , p. 135-162