Actuarial Seminar - Alan Xian (Macquarie)

Title: Understanding and predicting large time series with Markov-modulated non-homogeneous Poisson processes
Abstract: This research seeks to deal with an important practical issue in modelling large time series data sets, such as those found in insurance, in that the practitioner is often able to rely on some domain knowledge or past experience to inform the modelling process. However, it is also unlikely that all drivers of events of interest are able to be adequately captured by a practitioners chosen model due to data limitations and materiality concerns.
We propose the usage of the usage of Markov-modulated non-homogeneous Poisson processes to examine counting processes. The modelling framework proposed is applicable to a variety of different modelling contexts, although specific innovations are implemented to deal with large data sources. This approach serves to link the modellable factors (allowing much flexibility in terms of model choice) with unmodellable/hard-to-model factors through the use of a hidden Markov structure.
In previous work, we have shown that this methodology performs well for in-sample analysis, including accurate calibration and filtering of the hidden regimes. In this presentation, we will instead largely focus on out-of-sample prediction. In particular, we place some emphasis on the forecast distribution as this is of great importance for various actuarial exercises in practice such as reserving and capital management, as well as the calculation of tail-based risk measures. It is empirically demonstrated using real Australian insurance data that our proposed method can provide superior predictive distributional performance in many different actuarial claims prediction contexts.
This is joint work with Benjamin Avanzi (University of Melbourne), Greg Taylor (UNSW), and Bernard Wong (UNSW).