I will present a new approach to the problem of optimal contract design which is based on a relaxation of the control problem of the agent. Under the assumption of compactness of the set of admissible contracts, we establish existence of a solution to the so-called ``relaxed" optimal contract problem in the models where the state process is given by a multidimensional diffusion with linearly controlled drift. Then, under certain convexity assumptions, we show that the optimal contracts in relaxed formulation also solve the associated strong optimal contract problem. The main advantages of this approach, relative to the existing methods, are due to the fact that it allows (i) to obtain the existence of an optimal contract (as a limit point of epsilon-optimal ones), and (ii) to include various additional constraints on the associated control problems (e.g., state constraints, difference in filtrations of the agent and of the principal, etc.). These advantages make this approach well suited for the problem of optimal brokerage fees, in which a client of a broker has access to a larger filtration (representing the proprietary trading signal of the client). I will show how the latter problem can be solved using the relaxed control approach. This is a joint work with G. A. Alvarez.
Short Bio: Sergey Nadtochiy is a Professor of Applied Mathematics at Illinois Tech. Prior to this he was an Assistant Professor in Mathematics at University of Michigan and a Research Fellow in Oxford-Man Institute at Oxford University. Sergey received his PhD from Princeton University in the Department of Operations Research and Financial Engineering in 2009 and his undergraduate degree from Moscow State University (Math) in 2005. In his research, Sergey solves problems in Probability and PDEs motivated by applications in Finance/Economics, Physics and Statistics.