FINITE DIFFERENCE METHODS FOR PRINCIPAL-AGENT PROBLEM WITH LEARNING: MORAL HAZARD CASE

Abstract

This master thesis describes the Principal-Agent problem in a continuous-time setting. The principal hires the agent to manage a project and provides incen- tives by designing a contract. In the moral hazard case, the outcome process is driven by the agent’s e ort, unobservable to the principal. The contribution of this thesis is to study the influence of an exogenous parameter interpreted as e ect of good or bad economic contexts on the optimal contract. The princi- pal appreciates the e ect of this parameter by observing the perturbed output filtered as a learning process. In particular, under the infinite-horizon Marko- vian framework, BSDEs system can be reduced to a unique HJB equation that characterizes the optimal contract. HJB solutions are computed numerically by finite di erence methods. By developing both explicit and implicit schemes, we study how the principal’s profit, the agent’s e ort and the optimal contract fluctuate with the learning parameter and the output volatility.