To meet future liabilities general insurance companies will set up reserves. Predicting future cash flows is essential in this process. The vast literature on (stochastic) loss reserving methods concentrates on data aggregated in run off triangles. However, a triangle is a summary of an underlying data set with the development of individual claims. We refer to this data set as micro level data. Antonio & Plat (SAJ, 2014) develop a time-continuous model for such micro-level data, following the probabilistic framework of Norberg (1993, 1999). Their proposed model, however, assumes the availability of time-continuous data for the claim development process, a level of granularity which is not necessarily present within many insurance companies. Therefore, the work by Antonio and Plat (2014) was extended to also deal with time-discrete data. To this end, a multiple state framework is proposed, such that the claim development process can be reconstructed as a series of transitions between a given set of states. The transition probabilities between the latter states are modeled by means of a multinomial regression model, hereby allowing the transition probabilities to depend on, if necessary, time-varying covariates. A second extension of the work by Antonio and Plat (2014) is proposed regarding the claim size distribution. For each payment made during the claim development process, a flexible payment distribution is modeled. We hereby explicitly incorporate inflation effects. In Antonio and Plat (2014), a standard parametric distribution was chosen to model the complete support of the payment distribution. Here we use an approach based on splicing: the distribution is divided in slices and by means of a multinomial distribution the probability is determined that a certain payment pertains to the slice of interest. The different slices themselves are modeled by means of truncated gamlss models (Rigby and Stasinopoulos, 2005) and the best fitting truncated distribution is determined from the large library of the gamlss error distributions by means of the Akaike Information Criterion (AIC).
(Joint work with dr. Robin Van Oirbeek and Els Godecharle, both at KU Leuven)