Fitting Nonstationary Cox Processes : An application to fire insurance data

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      <subfield code="a">Albrecher, Hansjörg</subfield>
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      <subfield code="a">Fitting Nonstationary Cox Processes</subfield>
      <subfield code="b">: An application to fire insurance data</subfield>
      <subfield code="c">Hansjorg Albrecher, José Carlos Araujo-Acuna, Jan Beirlant</subfield>
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      <subfield code="a">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.</subfield>
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      <subfield code="t">North American actuarial journal</subfield>
      <subfield code="d">Schaumburg : Society of Actuaries, 1997-</subfield>
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      <subfield code="g">01/06/2021 Tomo 25 Número 2 - 2021 , p. 135-162</subfield>
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