Optimal Contracts and Optimal Stopping

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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.