Forecasting of Insurance Claim Distributions using Markov-modulated non-homogeneous Poisson Pprocesses

The Markov-modulated homogeneous Poisson process is utilised in a variety of fields including the natural sciences, economics, finance and operational research. The hidden regime structure allows for sudden changes in frequency in a tractable manner. However, the predictive capabilities of this approach are hampered by several shortcomings and we propose a non-homogeneous extension known as the Markov-modulated non-homogeneous Poisson process to resolve these issues.

This approach is attractive as it provides a flexible  that is able to accommodate a wide variety of underlying drivers of frequency observations, using both the original hidden regime-switching structure alongside a malleable frequency perturbation measure.  This means that the proposed method can be adapted to many different modelling problems. We show that our framework is particularly advantageous in big data problems where practitioners need to account for significant numbers of interactions.

To validate theoretical findings, we provide several case studies on a large Australian insurance data sets to demonstate the advantages of such an approach for generating predictive distributions, as compared to more standard actuarial methods. Comparisons are made through probabilistic forecasting techniques that show that the forecasts generated by this approach provide better distributional accuracy. This is important in actuarial contexts where various quantiles are under consideration such as the calculation of risk margins or tail-based risk measures.