For many economic processes effects caused by time delay play an important role. Besides empirical evidence there are many theoretical macroeconomic models taking account of delay factors like "time to build", "vintage capital" or "information lags". In addition to the randomness of future shocks these time delays are another source of uncertainty for economic agents. Exactly this combination of exogenous stochastic inputs and delay factors gives rise to risks that are difficult ot handle due to the non-feasibility of instantaneous reactions to a changed environment. Typical consequences are oscillations caused by oversteering or in general more conservative strategies and policies.
The aim of this project is to determine optimal policies for stochastic models under time delay modeled in continuous time, in particular for applications in economic growth theory. Because of the loss of the Markov property standard optimisation techniques yield infinite dimensional problems which have so far been investigated only in very special cases.
Based on economic motivation the research will yield new insights with respect to implications of time delay for economic processes as well as with respect to the mathematical model analysis. In the concrete case of economic growth theory standard models will be extended by stochastic and delay factors and their economic impact will be investigated. In addition to qualitative statements we will also focus on quantitative results for which numerical implementations and the development of statistical procedures for model calibration will be of key importance. Mathematically, explicit solutions for simple models will be sought and approximate solution algorithms will be studied. Finally, in interaction with other projects models from different economic areas will be studied with regard to the qualitative and quantitative impact of time delay.