  Forecasting costs is now a front burner in empirical economics. We propose an
unconventional tool for stochastic prediction of future expenses based on the
individual (micro) developments of recorded events. Consider a firm,
enterprise, institution, or state, which possesses knowledge about particular
historical events. For each event, there is a series of several related
subevents: payments or losses spread over time, which all leads to an
infinitely stochastic process at the end. Nevertheless, the issue is that some
already occurred events do not have to be necessarily reported. The aim lies in
forecasting future subevent flows coming from already reported, occurred but
not reported, and yet not occurred events. Our methodology is illustrated on
quantitative risk assessment, however, it can be applied to other areas such as
startups, epidemics, war damages, advertising and commercials, digital
payments, or drug prescription as manifested in the paper. As a theoretical
contribution, inference for infinitely stochastic processes is developed. In
particular, a non-homogeneous Poisson process with non-homogeneous Poisson
processes as marks is used, which includes for instance the Cox process as a
special case.
