The dynamics of state variables of an economic system are described using stochastic differential equations. The system is observed in discrete points of time in order to get information about the status of the state variables. The gained information leads to decisions that are implemented in order to get optimal results e.g. maximum utility. Some state variables cannot be observed at all and about other only partial information can be obtained. After taking measurements the information about the status of the state variables is updated. The optimal number of measurements is determined using active learning concept. The model can be used to determine optimal managerial and economic issues related to life-cycle length, e.g. life cycle of a product, the length of a production process over time.
