In this paper we put forward a new model to compute the loss distri- bution of an automobile insurance company’s portfolio evolving by a bonus-malus system. We allow for a continuous evolution of the demographic-economic system based on a migration’s rule which is refreshed in discrete time, i.e. at the monitor- ing times . Therefore the migration’s probabilities are discretely updated through a technique based on the combinatorial distributions of claims’ arrival in the rat- ing classes. This technique is hierarchical copula-based, a natural tool permitting us to represent the co-movement between claims’ arrivals, and distorted due to the formalization of an arrival policy of claims, that restricts the set of combi- natorial distributions to those representing the most probable scenarios, therefore distorting the loss function. At every monitoring date the copula-based model com- putes the migration’s probabilities and the loss function which accommodates for a discrete-time dynamic of the claims’ reserving and the capital requirements. As an empirical application, we study the problem of evaluating the claims’ reserving and the capital requirements for different kinds of hierarchies, based on real data originating with the General Insurance Association of Singapore.