Optimal Compensation and Pay‐Performance Sensitivity in a Continuous‐Time Principal‐Agent Model

This paper studies the optimal contract between risk‐neutral shareholders and a constant relative risk‐aversion manager in a continuous‐time model. Several interesting results are obtained. First, the optimal compensation is increasing but concave in output value if the manager is more risk averse than a log‐utility manager. Second, when the manager has a log utility, a linear contract is optimal when there is no explicit lower bound on the compensation, and an option contract is optimal when there is an explicit lower bound. Third, optimal effort is stochastic (state dependent). Fourth, consistent with empirical findings and contrary to standard agency theory predictions, the relationship between pay‐performance sensitivity and firm performance and that between pay‐performance sensitivity and firm risk can be nonmonotonic.