Challenges in Stochastic Control, Information and Applications (completed)
About the project
- What is the optimal sustainable harvesting strategy from a fish population?
- What is the best portfolio choice in a financial market?
These are examples of problems that can be studied by using stochastic differential equations (SDEs), which are differential equations subject to uncertainty or "noise". Today there is a well-established theory for optimal control of systems described by SDEs, but this theory is based on a number of restrictive assumptions, such as
(i) the Markov property (i.e. lack of memory) of the system and
(ii) that the controller has at any time access to full information about the current state of the system at the time, nothing more and nothing less.
These assumptions are, however, not satisfied in many important situations. For example, the system or the control process might be subject to delay. Or the system dynamics might depend not just on the current state of the system, but also on the probabilistic law of the state (such systems are called mean-field systems). Or the controller might have access only to partial information about the system, or about the future of the system (such controls are called insider controls).
What is the optimal control then? How does the available information flow effect the optimal performance?
These problems are beyond the state-of-the-art of the theory, and new ideas are needed to handle them. It is the purpose of this project to meet the challenges that these problems represent. In particular, we want to develop new theories and methods based on combinations of white noise theory and generalized Malliavin calculus, for the solution of the optimal control problems of stochastic systems with memory, mean-field systems, and systems where the controller has either partial information or inside information, or a combination. The results will be applied to stochastic control problems in several areas, including physics, biology and finance.
Research council of Norway, Independent projects - project number 250768. Total budget approx 11 mill NOK.