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A MARKED COX MODEL FOR THE NUMBER OF IBNR CLAIMS: ESTIMATION AND APPLICATION

Published online by Cambridge University Press:  28 May 2019

Andrei L. Badescu ,
Tianle Chen ,
X. Sheldon Lin  and
Dameng Tang
Andrei L. Badescu*
Affiliation:
Department of Statistical Sciences University of Toronto100 St. George Street Toronto, ON M5S 3G3, Canada E-Mail: badescu@utstat.toronto.edu
Tianle Chen
Affiliation:
Department of Statistical Sciences University of Toronto100 St. George Street Toronto, ON M5S 3G3, Canada E-Mail: tianlechen@gmail.com
X. Sheldon Lin
Affiliation:
Department of Statistical Sciences University of Toronto100 St. George Street Toronto, ON M5S 3G3, Canada E-Mail: sheldon@utstat.toronto.edu
Dameng Tang
Affiliation:
Department of Statistical Sciences University of Toronto100 St. George Street Toronto, ON M5S 3G3, Canada E-Mail: dameng.tang@mail.utoronto.ca
*
E-Mail: badescu@utstat.toronto.edu
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Abstract

Incurred but not reported (IBNR) loss reserving is of great importance for Property & Casualty (P&C) insurers. However, the temporal dependence exhibited in the claim arrival process is not reflected in many current loss reserving models, which might affect the accuracy of the IBNR reserve predictions. To overcome this shortcoming, we proposed a marked Cox process and showed its many desirable properties in Badescu et al. (2016).

In this paper, we consider the model estimation and applications. We first present an expectation–maximization (EM) algorithm which guarantees the efficiency of the estimators unlike the moment estimation methods widely used in estimating Cox processes. In addition, the proposed fitting algorithm can be implemented at a reasonable computational cost. We examine the performance of the proposed algorithm through simulation studies. The applicability of the proposed model is tested by fitting it to a real insurance claim data set. Through out-of-sample tests, we find that the proposed model can provide realistic predictive distributions.

Keywords

IBNR claimsloss reservingCox modelhidden Markov chaintemporal dependencePascal mixtureEM algorithm
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 3 , September 2019 , pp. 709 - 739
Copyright
© Astin Bulletin 2019 

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