"For almost all kinds of dynamic systems modeling real processes in nature or society, most of the mathematical models we can formulate are - at best - inaccurate, and subject to random fluctuations and other types of ""noise"". Therefore it is important to be able to deal with such noisy models in a mathematically rigorous way. This rigorous theory is stochastic analysis. Theoretical progress in stochastic analysis will lead to new and improved applications in a wide range of fields.The main purpose of this proposal is to establish a research environment which enhances the creation of new ideas and methods in the research of stochastic analysis and its applications. The emphasis is more on innovation, new models and challenges in the research frontiers, rather than small variations and minor improvements of already established theories and results. We will concentrate on applications in finance and biology, but the theoretical results may as well apply to several other areas.Utilizing recent results and achievements by PI and a large group of distinguished coworkers, the natural extensions from the present knowledge is to concentrate on the mathematical theory of the interplay between stochastic analysis, stochastic control and information. More precisely, we have ambitions to make fundamental progress in the general theory of stochastic control of random systems and applications in finance and biology, and the explicit relation between the optimal performance and the amount of information available to the controller. Explicit examples of special interest include optimal control under partial or delayed information, and optimal control under inside or advanced information. A success of the present proposal will represent a substantial breakthrough, and in turn bring us a significant step forward in our attempts to understand various aspects of the world better, and it will help us to find optimal, sustainable ways to influence it."