Continuous-time Principal-Agent Problem

Prof. Nizar Touzi

Ecole Polytechnique

About the Speaker

Nizar Touzi is Professor of Applied Mathematics at Ecole Polytechnique since 2006. He was previously Chair Professor at Imperial College London. He was an invited session speaker at the International Congress of Mathematicians (Hyderabad 2010). He received the Louis Bachelier prize of the French Academy of Sciences in 2012, and the Paris Europlace prize of Best Young Researcher in Finance in 2007. In 2010, he held the University of Toronto Dean's Distinguished Chair position. He is Co-editor and Associate Editor in various international journals in the fields of financial mathematics, applied probability, and control theory.

Abstract

The Principal-Agent problem is the corner stone for the modeling of optimal incentive schemes to account for moral hasard in economics. We provide a systematic method for solving such stackelberg game problems in the continuous time setting. Our approach is the following: we first find the contract that is optimal among those for which the agent's value process allows a dynamic programming representation, in which case the agent's optimal effort is straightforward to find. We then show that the optimization over the restricted family of contracts represents no loss of generality. As a consequence, the non-zero sum stochastic differential game reduces to a stochastic control problem which may be addressed by standard tools of control theory. Our arguments rely on the backward stochastic differential equations approach to non-Markovian stochastic control, and more specifically, on the recent extensions to the second order case.