FACULTÉ & RECHERCHE

This paper seeks to characterize incentive compensation in a static principal–agent moral hazard setting in which both the principal and the agent are prudent (or downside risk averse). We show that optimal incentive pay should then be “approximately concave” in performance, the approximation being closer the more downside risk averse the principal is compared with the agent. Limiting the agent’s liability would improve the approximation, but taxing the principal would make it coarser. The notion of an approximately concave function we introduce here to describe optimal contracts is relatively recent in mathematics, it is intuitive and translates into concrete empirical implications, notably for the composition of incentive pay packages. We also clarify which measure of prudence—among the various ones proposed in the literature—is relevant to investigate the tradeoff between downside risk sharing and incentives.