New perspectives in contract theory: Optimal incentives for interacting agents in a common random environment

契约理论的新视角：共同随机环境中交互主体的最优激励

• 批准号: 2307736
• 负责人: Emma Hubert
• 金额: $ 26万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2307736&HistoricalAwards=false
• 关键词: New; perspectives; contract; theory; Optimal

Continuous-time principal-agent problems offer a relevant mathematical framework for the study of optimal incentives between agents, especially with information asymmetry. In the seminal model by Holmström and Milgrom (1987), a principal (she) is imperfectly informed about the actions of an agent (he) on a random process representing the value of a project over time. To incentivize the agent to act in her best interest, she can offer him a contract, namely a terminal payment indexed on the value of the project. These problems are fundamentally related to the design of optimal incentives and are therefore present in a wide variety of situations, including not only economics but also politics, finance, etc. Although this theory has been extended to allow the principal to contract with many agents, the possibility that agents may be impacted by common hazards and risks is currently mostly neglected. This research focuses on the development of principal-agent problems to incorporate the fact that the agents may live in a common uncertain environment and may interact with each other but also with this environment. This research theme is motivated by several concrete applications, where this common uncertain environment cannot be neglected when looking for the optimal actions or incentives to implement, e.g., optimization of electricity production and consumption, regulation of financial and systemic risks, or design of optimal and sustainable insurance policies. The themes are at the heart of current economical and societal challenges, both nationally and internationally. Studying them in a quantitative way can therefore help inform public policy, and thus contribute to the achievement of societally relevant outcomes. This research will also have an essential mentoring orientation, involving graduate students from the Operations Research & Financial Engineering Graduate Program, who will be partially supported by the funds awarded.Considering a common random environment induces a wide range of additional mathematical difficulties, which have only been recently addressed, albeit only for pure mean-field games. To address this type of general problem, technical results will be further developed, notably on second order backward stochastic differential equations (2BSDEs), which are typically used to determine the optimal form of contracts in principal-agent problems. To consider general multi-agent problems with Nash or mean-field interactions, it is necessary to develop generalized notions of 2BSDEs, namely multidimensional or mean-field 2BSDEs. Moreover, even in a classical framework, the idea of considering common jumps in a multi-agent or mean-field setting has never been investigated, despite its relevance to model collective accidents such as climatic hazards and will involve the study of (multidimensional or mean-field) 2BSDEs with jumps. Finally, with the idea of ensuring the implementation of realistic contracts, a principal’s problem with constraints on the contract can be reformulated as a stochastic target problem. These theoretical developments will considerably advance knowledge in the field of 2BSDE and more broadly of stochastic control and will allow the study of the various applications.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.

连续时间委托代理问题为研究代理人之间的最优激励，特别是在信息不对称的情况下，提供了一个相关的数学框架。在Holmström和Milgrom（1987）的开创性模型中，委托人（她）不完全了解代理人（他）在代表项目随时间价值的随机过程中的行为。为了激励代理按照自己的最佳利益行事，她可以向代理提供一份合同，即一笔与项目价值挂钩的终端付款。这些问题从根本上与最佳激励的设计有关，因此存在于各种各样的情况中，不仅包括经济，还包括政治、金融等。虽然这一理论已被扩展到允许委托人与许多代理人签订合同，但代理人可能受到共同危害和风险影响的可能性目前大多被忽视。本研究的重点是委托代理问题的发展，以考虑代理可能生活在一个共同的不确定环境中，并且可能相互作用，但也可能与这个环境相互作用。本研究主题是由几个具体的应用驱动的，在寻找最佳行动或激励措施时，这种常见的不确定环境不能被忽视，例如，优化电力生产和消费，监管金融和系统风险，或设计最佳和可持续的保险政策。这些主题是当前国内和国际经济和社会挑战的核心。因此，以定量的方式研究它们有助于为公共政策提供信息，从而有助于实现与社会相关的成果。这项研究也将有一个重要的指导导向，包括来自运筹学与金融工程研究生项目的研究生，他们将获得部分资助。考虑一个普通的随机环境会引发一系列额外的数学难题，这些问题直到最近才得到解决，尽管只是针对纯粹的平均场博弈。为了解决这类一般性问题，将进一步发展技术成果，特别是二阶后向随机微分方程（2BSDEs），它通常用于确定委托-代理问题中合同的最佳形式。为了考虑具有纳什或平均场相互作用的一般多智能体问题，有必要发展2BSDEs的广义概念，即多维或平均场2BSDEs。此外，即使在经典框架中，考虑多智能体或平均场设置中常见跳跃的想法从未被研究过，尽管它与气候灾害等模型集体事故相关，并且将涉及具有跳跃的（多维或平均场）2BSDEs的研究。最后，在保证现实契约执行的前提下，委托人的契约约束问题可以重新表述为随机目标问题。这些理论的发展将大大推进2BSDE领域的知识和更广泛的随机控制领域的知识，并将允许对各种应用的研究。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。