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 and so linear contracts maximize profit. If the agent is risk averse, the concavity constraint might bind for some outputs but not others. We characterize the unique profit-maximizing contract and show how deterring risk-taking affects the insurance-incentive trade-off. Our logic extends to costly risk-taking and to dynamic settings where the agent can shift output over time.

中文翻译：

---

与风险承担者的最优合同

考虑一个可以在其输出中无成本地添加均值保持噪声的代理。为了阻止这种冒险行为，委托人最好提供一个合同，使代理人的效用在输出中呈凹形。如果代理人是风险中性的并受到有限责任的保护，则这种凹面约束将具有约束力，因此线性合同使利润最大化。如果代理是风险厌恶的，则凹度约束可能对某些输出有约束力，但对其他输出则没有约束力。我们描述了独特的利润最大化合同，并展示了阻止风险承担如何影响保险激励权衡。我们的逻辑扩展到代价高昂的冒险和动态设置，代理可以随着时间的推移改变输出。