Journal article

Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework

Benjamin Avanzi, Greg Taylor, Bernard Wong, Alan Xian

European Journal of Operational Research | Elsevier BV | Published : 2020

Abstract

The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of observed event arrivals to be naturally incorporated in a tractable manner, while the hidden Markov chain captures the effect of unobservable drivers of the data. In addition to increases in accuracy and interpretability, this method supplements analysis of the latent factors. Further, this procedure naturally incorporates data features such as ov..

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University of Melbourne Researchers

Grants

Awarded by Australian Research Council


Awarded by Suncorp Metway Ltd


Funding Acknowledgements

The authors are grateful to two anonymous referees for detailed comments, which led to substantial improvements to the paper. Earlier versions of this paper were presented at the 8th and 9th Australasian Actuarial Education and Research Symposium in Sydney (Australia), the 22nd International Congress on Insurance: Mathematics and Economics in Sydney (Australia), the Actuarial Risk Modelling and Extreme Values Workshop in Canberra (Australia), the 4th European Actuarial Journal Conference in Leuven (Belgium), the ASTIN Colloquium in Cape Town (South Africa) as well as at seminars held at the universities of Lyon and Copenhagen in 2019. Some results in this paper were also presented at the Australian Actuaries Institute General Insurance Seminar in November 2018 (and awarded the Taylor Fry Silver Award); see Avanzi et al. (2018). The authors are grateful for constructive comments received from colleagues who attended these events. 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 (DP200101859) Projects funding schemes. Furthermore, Alan Xian acknowledges financial support by the Australian Government Research Training program, as well the UNSW Business School through supplementary scholarships. The views expressed herein are those of the authors and are not necessarily those of the supporting organisations.