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

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