Optimal Brokerage Contract in Almgren-Chriss mode

Speaker:

Guillermo Alonso Alvarez, Ph.D. student, Department of Applied Mathematics, Illinois Tech

Description:

The role of the broker in the market is to produce transactions for an Investor charging them a fee which usually depends on the performance of the Investor in return for better conditions as lower market impact or anonymity. From a rational point of view, the goal of the broker is to set a fee that maximizes a given performance measure while their client invests optimally. Mathematically, optimal brokerage problems can be viewed as Stochastic Optimal Contract Problems where the Broker is the Principal and the Investor is the Agent. 
Under the Almgren-Chriss market impact model we found a collection of optimal fees using the results of Cvitanic, Possamaï and Touzi in “Dynamic programming approach to Principal-Agent problems” when Broker and Investor are risk neutral and the Investor has the option to bypass the Broker trading directly. The essential idea of our solution is to use the weak formulation of Stochastic Control Problems and first and second order BSDEs to represent fees as solutions of controlled forward stochastic differential equations. 

 

Mathematical Finance, Stochastic Analysis, and Machine Learning