2018/03/23 by Nicolás Hernández Santibáñez, Santibánez, Nicolás Hernández, Thibaut Mastrolia +1 · 2 citations
Economics, Econometrics and Finance · #49L25 #91A15 #93E20 #Economic theories and models #FOS: Mathematics #Law, Economics, and Judicial Systems #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1803.08951
openalex publication_date 2018/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate a Principal-Agent problem with moral hazard under Knightian uncertainty. We extend the seminal framework of Holmström and Milgrom by combining a Stackelberg equilibrium with a worst-case approach. We investigate a general model in the spirit of Cvitanić, Possamaï and Touzi (2018). We show that optimal contracts depend on the output and its quadratic variation, as an extension of the works of Mastrolia and Possamaï (2016) (by dropping all the restrictive assumptions) and Sung (2015) (by considering a general class of admissible contracts). We characterize the best reaction effort of the agent through the solution to a second order BSDE and we show that the value of the problem of the Principal is the viscosity solution of an Hamilton-Jacobi-Bellman-Isaacs equation, without needing a dynamic programming principle, by using stochastic Perron's method.