A Marked Cox Model for the Number of IBNR Claims: Estimation and Application

Astin Bulletin, 1-31. doi:10.1017/asb.2019.15

31 Pages Posted: 14 Mar 2016 Last revised: 7 Jun 2019

See all articles by Andrei Badescu

Andrei Badescu

University of Toronto - Department of Statistics

X. Sheldon Lin

Department of Statistical Sciences, University of Toronto

Dameng Tang

University of Toronto

Date Written: March 14, 2016

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. (2015b).

In this paper, we consider the model estimation and applications. We first present a generalized 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 more realistic predictive distributions when compared with some traditional reserving model. Finally, we investigate and show the importance of introducing the temporal dependence in the proposed model.

Keywords: IBNR Claims; Loss Reserving; Cox Model; Hidden Markov Chain; Temporal Dependence; Pascal Mixture; EM Algorithm

JEL Classification: C13, C14, C63

Suggested Citation

Badescu, Andrei and Lin, Xiaodong Sheldon and Tang, Dameng, A Marked Cox Model for the Number of IBNR Claims: Estimation and Application (March 14, 2016). Astin Bulletin, 1-31. doi:10.1017/asb.2019.15, Available at SSRN: https://ssrn.com/abstract=2747223 or http://dx.doi.org/10.2139/ssrn.2747223

Andrei Badescu

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

Xiaodong Sheldon Lin (Contact Author)

Department of Statistical Sciences, University of Toronto ( email )

Department of Statistical Sciences
100 St George Street
Toronto, Ontario M5S 3G3
Canada

Dameng Tang

University of Toronto ( email )

105 St George Street
Toronto, Ontario M5S 3G8
Canada

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