Consider an agent who can costlessly add mean-preserving noise to his output. To deter such risk-taking, the principal optimally offers a contract that makes the agent's utility concave in output. If the agent is risk-neutral and protected by limited liability, this concavity constraint binds...

We study a dynamic contracting problem in which size is relevant. The agent may take on excessive risk to enhance short-term gains, which exposes the principal to large, infrequent losses. To preserve incentive compatibility, the optimal contract uses size as an instrument; there is downsizing...