Fitting Nonstationary Cox Processes: An Application to Fire Insurance Data

Authors:
Publisher website
Google Scholar
Abstract
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 Selch, D. , and M. Scherer. 2018. A multivariate claim count model for applications in insurance. Switzerland: Springer Actuarial, Springer Nature Switzerland AG. [Crossref] , [Google Scholar] ) 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.
Funding Information
  • Swiss National Science Foundation Project (200021_168993)

This publication has 31 references indexed in Scilit: