Moral Hazard Under Ambiguity

In this paper, we extend the classical Holmstrom and Milgrom contracting problem, by adding uncertainty on the volatility of the output for both the Agent and the Principal. We study more precisely the impact of the Nature playing against the Agent and the Principal, by choosing the worst possible volatility of the output. We solve the first-best and the second-best problems in this framework, and we show that optimal contracts are in a class of contracts linear with respect to the output and its quadratic variation. We also present a general modus operandi to apply our method.