We propose a dynamical model to study multivariate time series with positive increments. The equation of motion accounts for the interactions among the series and contains both an inhomogeneous external field and a noise term. It is shown how the model can be exactly solved in absence of causal loops among the series and the general case is numerically investigated. The model can be naturally applied to the study of operational risk inside banks identifying each series with the time evolution of the money losses generated in different channels (human error, machinery failures, failed transactions), and the external field with the support given by the bank to each channel. In this context it is finally shown how some parameters of the model can be learned from a database of historical operational losses.