The estimation of claim and premium reserves is a key component of an actuary's role and plays a vital part of any insurance company's operations. In practice, such calculations are complicated by the stochastic nature of the claims process as well as the impracticality of capturing all relevant and material drivers of the observed claims data. In the past, computation limitations have promoted the prevalence of simplified, but possibly sub-optimal, aggregate methodologies. However, in light of modern advances in processing power, it is viable to increase the granularity at which we analyse insurance datasets so that potentially useful information is not discarded. By utilising more granular data that is usually readily available to insurers, model results and predictions may become more accurate and precise.
Unfortunately, detailed analysis of large insurance data sets in this manner poses some unique challenges. Firstly, there is no standard framework to which practitioners can refer and it may be challenging to tractably integrate all modelled components into one comprehensive model. Secondly, computation requirements are a material concern when processing such large volumes of data. Finally, analysis at this greater level of detail requires more intense scrutiny as trends and drivers that were previously masked by aggregation may emerge. This is particularly an issue with claim drivers that are either unobservable to the modeller or very difficult to model.
We propose a Markov-modulated non-homogeneous Poisson model to overcome the above problems in the practical implementation of a detailed "micro-level" claim count model. We incorporate a flexible exposure measure to explicitly allow for known claim drivers while the hidden component of the Hidden Markov model captures the impact of unobservable or practicably non-modellable information. Theoretical findings are illustrated and validated in an empirical case study using Australian non-life insurance data in order to highlight the benefits of the proposed approach.