  We suggest a general method for analyzing aggregate insurance claims that
arrive according to a very general point process, known in the literature as
the order statistic point process, which includes as special cases the
classical compound Poisson and the Sparre Andersen models, among many others.
We also allow for the process to govern claim sizes via a general dependence
structure that relates claim sizes to claim and/or inter-claim times. The
obtained general results are supplemented with special closed-form illustrative
formulas, that also exemplify the potential for future research in the area.
