In the first part of the talk, we will discuss a new proposed methodology, called adaptive robust control, for solving a discrete-time Markovian control problem subject to Knightian uncertainty. We general framework will be applied to a financial hedging problem where the uncertainty comes from the fact that the true law of the underlying model is only known to belong to a certain family of probability laws. We introduce a learning algorithm that reduces the model uncertainty through progressive learning about the unknow system. We will also derive the corresponding Bellman system of equations. One of the pillars in the proposed methodology is the recursive construction of the confidence sets for the unknown parameter, which will be discussed in the second part of the talk.

Igor Cialenco received his PhD in Applied Mathematics from University of Southern California, after which he joins as permanent faculty the Department of Applied Mathematics at Illinois Institute of Technology. Currently, his primary research interests are in mathematical finance, statistical inference for SPDEs and stochastic control.