Optimal Contracts and Optimal Stopping

在过去的几十年里，最优契约理论一直是经济学文献的核心，在许多领域都有应用，包括资产管理、保险、共享经济、税收和远程医疗。最优契约的目标是激励代理人披露委托人无法观察到的正在进行的项目的真实状态，并使委托人的福利最大化。同时，它还保证代理商对补偿感到满意，无论是由于法规还是与替代机会相比。PI计划分析如何在委托代理关系中最优地设计和终止合同补偿，以及由于双方之间的信息不对称而导致的潜在道德风险。预期的结果有助于我们理解不同契约下代理人的行为，并在实践中有具体的应用，例如，资产管理公司为其投资者选择的投资组合的风险暴露，以及保单持有人的退出行为，这两者都有助于监管和设计金融产品，改善市场参与者之间的福利分配。研究的主题包括：（i）同时规定补偿和终止规则的最优契约，关系型合同没有具体的终止规则，但可以由委托人或代理人终止。我们的目标是开发新的工具，并加强现有的最优合同理论，以纳入最优停止，跳跃扩散和代理谁控制状态变量的扩散系数，例如动态规划方法，将一个最优合同问题与停止到一个随机控制/停止问题，以及在关系合同只能由当事人终止的情况下对可接受性的新定义，这保证了代理人对每个可接受合同的响应是明确定义的，并且对委托人采用的任意停止时间是鲁棒的。其中一些结果有助于证明和解释在以前的文献中普遍存在的假设，例如通常的资产管理公司的提款限制，并使最优合同理论更接近于practice.This奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

The theory of optimal contracts has been central in economics literature over the past few decades, with applications in many areas, including asset management, insurance, sharing economy, taxation, and telemedicine. The optimal contract is supposed to incentivize the agents to reveal the true status of the ongoing projects, which is not always observable by the principal, and to maximize the welfare of the principal. At the same time, it also guarantees that the agents are satisfied with the compensation, either due to regulations or compared to alternative opportunities. The PI plans to analyze how contractual compensation are optimally designed and terminated in a principal-agent relationship, and the potential moral hazard due to the information asymmetry between the two parties. The expected results help us understand the agents' behavior under different contracts and have concrete applications in practice, for example, the risk exposure of portfolios chosen by asset managers for their investors, and the withdrawal behavior of insurance policy holders, both of which help regulate and design financial products, and improve welfare distribution among market participants.The research topics include (i) the optimal contracts which specify both the compensation and the terminating rule, and (ii) relational contracts with no specific rules on termination but can be stopped by either the principal or the agents. The goal is to develop new tools and strengthen existing ones in the optimal contract theory to incorporate optimal stopping, jump diffusions and agents who control the diffusion coefficient of the state variable, e.g. a dynamic programming approach which transform an optimal contract problem with stopping to a stochastic control/stopping problem, and a new definition for admissibility in the case of relational contracts that can only be terminated by the principal, which guarantees that the agent's response to each admissible contract is well-defined and robust to arbitrary stopping times adopted by the principal. Some of these results help justify and explain prevailing assumptions in the previous literature, for example the usual drawdown constraints for asset managers and make optimal contract theory closer to practice.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.