Journal article
On the modelling of multivariate counts with Cox processes and dependent shot noise intensities
Benjamin Avanzi, Greg Taylor, Bernard Wong, Xinda Yang
INSURANCE MATHEMATICS & ECONOMICS | ELSEVIER | Published : 2021
Abstract
In this paper, we develop a method to model and estimate several, dependent count processes, using granular data. Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of counts (e.g. insurance claims). The dependency structure is introduced via multivariate shot noise intensity processes which are connected with the help of Lévy copulas. In aggregate, our approach allows for (i) over-dispersion and auto-correlation within each line of business; (ii) realistic features involving time-varying, known covariates; and (iii) parsimonious dependence between processes without requiring simultaneous primary (e.g. accidents) events.
Related Projects (2)
Grants
Awarded by Australian Research Council
Awarded by Natural Science and Engineering Research Council of Canada
Funding Acknowledgements
This research was supported under Australian Research Council's Linkage (LP130100723, with funding partners Allianz Australia Insurance Ltd, Insurance Australia Group Ltd, and Suncorp Metway Ltd) and Discovery, Australia (DP200101859) Projects funding schemes. Furthermore, Avanzi acknowledges support from a grant of the Natural Science and Engineering Research Council of Canada (project number RGPIN-2015-04975). Finally, Yang acknowledges financial support from an Australian Postgraduate Award and supplementary scholarships provided by the UNSW Business School, Australia. The views expressed herein are those of the authors and are not necessarily those of the supporting organisations.