Abstract: Incurred but not reported (IBNR) loss reserving is a very important issue for Property & Casualty (P&C) insurers. To calculate IBNR reserve, one needs to model claim arrivals and then predict IBNR claims. However, factors such as temporal dependence among claim arrivals and exposure fluctuation are often not incorporated in most of the current loss reserving models, which greatly affect the accuracy of IBNR predictions. In this talk, I will present a new modelling approach under which the claim arrival process together with the reporting delays follows a marked Cox process. The intensity function of the Cox process is governed by a hidden Markov chain. I will show that the proposed model is versatile in modeling temporal dependence, can incorporate exposure fluctuation, and can be interpreted naturally in the insurance context. The associated reported claim process and IBNR claim process remain to be a marked Cox process with easily convertible intensity function and marking distribution. The specific structure of the intensity function allows for generating discretely observed claim processes, which is critical for data fitting purposes. Closed-form expressions for both the autocorrelation function (ACF) and the distributions of the numbers of reported claims and IBNR claims are derived. I will then present a generalized expectation-maximization (EM) algorithm to fit the model to data and to estimate the model parameters. The proposed model is examined through simulation studies and is applied to a real insurance claim data set. We compare the predictive distributions of our model with those of the over-dispersed Poisson model (ODP), a stochastic model that underpins the widely used chain-ladder method. The results show that our model can yield more accurate best estimates and more realistic predictive distributions. This is joint work with Andrei Badescu and Sheldon Lin.