  We analyze export data aggregated at world global level of 219 classes of
products over a period of 39 years. Our main goal is to set up a dynamical
model to identify and quantify plausible mechanisms by which the evolutions of
the various exports affect each other. This is pursued through a stochastic
differential description, partly inspired by approaches used in population
dynamics or directed polymers in random media. We outline a complex network of
transfer rates which describes how resources are shifted between different
product classes, and determines how casual favorable conditions for one export
can spread to the other ones. A calibration procedure allows to fit four free
model-parameters such that the dynamical evolution becomes consistent with the
average growth, the fluctuations, and the ranking of the export values observed
in real data. Growth crucially depends on the balance between maintaining and
shifting resources to different exports, like in an explore-exploit problem.
Remarkably, the calibrated parameters warrant a close-to-maximum growth rate
under the transient conditions realized in the period covered by data, implying
an optimal self organization of the global export. According to the model,
major structural changes in the global economy take tens of years.
