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

连续时间委托代理问题为研究代理人之间的最优激励提供了一个相关的数学框架，特别是在信息不对称的情况下。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）在代表项目价值随时间变化的随机过程中的行为。为了激励代理人按照她的最佳利益行事，她可以向他提供一份合同，即根据项目价值指数的终止付款。这些问题从根本上涉及到最优激励的设计，因此存在于各种各样的情况下，不仅包括经济学，而且还包括政治，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，代理人可能会受到共同的危害和风险的影响的可能性，目前大多被忽视。本研究的重点是委托代理问题的发展，以纳入这样一个事实，即代理人可能生活在一个共同的不确定的环境中，可能会相互作用，但也与这个环境。这个研究主题是由几个具体的应用，在寻找最佳行动或激励措施时，这种共同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，以定量方式研究这些问题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方向，涉及运筹学金融工程研究生课程的研究生，谁将部分由所授予的资金支持。考虑到一个共同的随机环境引起了广泛的额外的数学困难，这只是最近才得到解决，虽然只有纯平均场游戏。为了解决这种类型的一般问题，技术成果将进一步发展，特别是在二阶倒向随机微分方程（2BSDES），这是典型的用于确定最佳形式的合同在委托代理问题。考虑一般的多智能体问题与纳什或平均场相互作用，有必要发展广义的概念，即多维或平均场2BSDES。此外，即使在一个经典的框架中，考虑共同的跳跃在一个多智能体或平均场设置的想法从来没有被调查，尽管它的相关性模型集体事故，如气候灾害，将涉及研究（多维或平均场）2BSDES跳跃。最后，在保证现实契约执行的思想下，一个带有契约约束的委托人问题可以转化为一个随机目标问题。这些理论的发展将大大推进知识领域的2B和更广泛的随机控制，并将允许研究的各种应用程序。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

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.