A multivariate claim count model for applications in insurance. (English) Zbl 1417.91006

Selch, Daniela Anna; Scherer, Matthias

Springer Actuarial. Cham: Springer (ISBN 978-3-319-92867-8/hbk; 978-3-319-92868-5/ebook). xii, 158 p. (2018).

The monograph is an in-depth work concerning important topics in the actuarial field; it is designed to present a time-dynamic model for multivariate claim counts and its applications in the actuarial framework. Chapter 1 introduces the model, involving dependence across the components, over-dispersion and clustering of claims. In Chapter 2, the properties of the model are investigated and its dynamics are fully characterized. The estimation of the process parameters is treated in Chapter 3, where an interesting application to the Danish fire insurance provides a performance analysis of the process. Moreover, in Chapter 4, the actuarial applications are discussed and some extensions are presented in order to improve the process performance in a wide range of actuarial applications. Finally the Appendix contains some recalls on the Poisson process and Lévy subordinators. The monograph represents a reference book for researchers and actuaries.

Reviewer: Emilia Di Lorenzo (Napoli)

MSC:

91-02	Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
91B30	Risk theory, insurance (MSC2010)
91B70	Stochastic models in economics
60J75	Jump processes (MSC2010)
62P05	Applications of statistics to actuarial sciences and financial mathematics
60G51	Processes with independent increments; Lévy processes

Keywords:

claim number process; mixed Poisson process; claim arrival; dependent stochastic counting process; Lévy subordinator