Mathematical Finance, Stochastic Analysis and Machine Learning Seminar By Guillermo Alonso Alvarez - Optimal Contract Design via Relaxation: Application to the Problem of Brokerage Fees

Speaker: Guillermo Alonso Alvarez, Illinois Institute of Technology 

Title: Optimal Contract Design via Relaxation: Application to the Problem of Brokerage Fees. 

Abstract: I will present a new approach to show the existence of optimal contracts based on the relaxation of the agent's optimal control problem. Introducing the notion of "relaxed" controls of the agent we prove the existence of optimal contracts in models where the state is given by a diffusion process with linearly controlled drift. Under concavity assumptions we show that the "relaxed" optimal contracts solve their associated strong optimal contract problem. The main advantage of our model is that it allows us to (i) write an optimal contract as a limit of epsilon-optimal contracts, ii) show the existence of optimal contracts for non-standard Principal-Agent problems (state constraints or difference in flirtations between Principal and Agent). 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 client's trading signal). I will show how the latter problem can be solved using the relaxed control approach. This is a joint work with Sergey Nadtochiy.

 

Mathematical Finance, Stochastic Analysis and Machine Learning Seminar