Maximum principle and optimal control problems in economics

Optimal control problems arise in many fields of economics, in particular in problems of optimization of economic growth. The main distinctive feature of these problems is that the control process is considered on an infinite time interval. The infinite time horizon gives rise to some specific and challenging mathematical features of the problems. In particular, various “pathological” phenomena in the relations of the general version of the Pontryagin maximum principle can occur. In this talk we discuss a recently developed complete version of the Pontryagin maximum principle for infinite horizon optimal control problems. As a meaningful example, we consider a two-sector model of optimal economic growth subject to a random jump in prices.