Thursday 9 March 2023 – 3:15pm-4:15pm

Gaussian Agency problems with memory and Linear Contracts

Stéphane Villeneuve, professor of applied mathematics, Toulouse School of Economics.




Can a principal still offer optimal dynamic contracts that are linear in end-of-period outcomes when the agent controls a process that exhibits memory?
We provide a positive answer by considering a general Gaussian setting where the output dynamics are not necessarily semi-martingales or Markov processes. We introduce a rich class of principal-agent models  that  encompasses dynamic agency models with memory. From the mathematical point of view, we develop a methodology to deal with the possible non-Markovianity and non-semimartingality of the control problem, which can no longer be directly solved by means of the usual Hamilton-Jacobi-Bellman equation. Our main contribution is to show that, for one-dimensional models, this setting always allows for optimal linear contracts in end-of-period observable outcomes with a  deterministic optimal level of effort.  In higher dimension, we show that linear contracts are still optimal when the effort cost function is radial and we quantify the gap between linear contracts and optimal contracts for more general quadratic costs of efforts.



Registration, please contact

📍 The seminar will take place at emlyon business School (Ecully campus) – Room Learning Lab – building B, 1st Floor.

Stéphane Villeneuve


Professor of applied mathematics, Toulouse School of Economics

BioStéphane Villeneuve is a professor of applied mathematics and former dean of the department of mathematics at University of Toulouse 1 Capitole, where he is affiliated with both Toulouse School of Management and TSE. He is also a member of the TSE-Partnership Foundation (TSE-P) where he coordinates the Chair on Market Risk and Value Creation sponsored by SCOR under the aegis of The Risk Foundation. His research focuses on stochastic methods in finance and their applications for dynamic contracting.