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、分享经济、税收和远程医疗。最优合同应该激励代理人披露正在进行的项目的真实状态，而这并不总是被委托人观察到的，并使委托人的福利最大化。同时，它还保证代理人对补偿感到满意，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契约薪酬，以及由于双方之间的信息不对称而导致的潜在道德风险。预期结果有助于我们理解代理人在不同契约下的行为，并具有具体的应用，例如资产管理公司为其投资者选择的投资组合的风险敞口，以及投保人的退出行为，这两者都有助于规范和设计金融产品，改善市场参与者之间的福利分配。研究主题包括：(I)同时规定补偿和终止规则的最优契约；(Ii)没有特定终止规则但可以由委托人或代理人停止的关系契约。其目的是开发新的工具并加强最优契约理论中的现有工具，以包括最优停止、跳跃扩散和控制状态变量扩散系数的代理，例如，将带有停止的最优契约问题转化为随机控制/停止问题的动态规划方法，以及在只能由委托人终止的关系契约情况下的可容许性的新定义，该定义保证代理人对每个允许的契约的响应是明确的并且对于委托人采用的任意停止时间是稳健的。其中一些结果有助于证明和解释先前文献中的主流假设，例如资产管理公司的常见减记限制，并使最优合同理论更接近实践。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.