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

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.