Centro de Documentacion de Fundación MAPFRE - Fitting Nonstationary Cox Processes : An application to fire insurance data

MAP20210024344

Fitting Nonstationary Cox Processes : An application to fire insurance data / Hansjorg Albrecher, José Carlos Araujo-Acuna, Jan Beirlant

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

En: North American actuarial journal. - Schaumburg : Society of Actuaries, 1997- = ISSN 1092-0277. - 01/06/2021 Tomo 25 Número 2 - 2021 , p. 135-162

1. Empresas de seguros . 2. Mercado de seguros . 3. Reclamaciones . 4. Seguro de incendio . 5. Cálculo actuarial . I. Araujo-Acuna, José Carlos . II. Beirlant, Jan . III. Título.