ABSTRACT This paper develops an optimal incentive compensation scheme for a project with a predetermined target but no fixed deadline. A principal sponsors the project and hires an agent to execute it, offering a lump‐sum payment that depends only on the project's completion time. The agent exerts a baseline effort level but may increase effort at a personal cost to accelerate progress, balancing the reward from completion against the cost of additional effort. The principal aims to maximize expected payoff, defined as the value of project completion minus the payment to the agent, while also internalizing the cost of delays. Project progress is modeled as a reflected Brownian motion with an agent‐controlled drift rate. We solve the associated Bellman equation to characterize the agent's optimal effort and derive the principal's optimal incentive scheme. Extensions include settings in which the agent faces a delay penalty or the principal discounts future rewards. These create additional trade‐offs between incentive provision and completion timing. Our numerical experiments further indicate that the principal's payoff is nonmonotonic in the payment level: very small payments produce slow completion, and excessively large payments reduce the net benefit. A finite‐horizon extension incorporates project termination at a fixed deadline, which further highlights the role of timing incentives. Throughout, we provide numerical illustrations and managerial insights for designing incentive contracts in target‐driven project environments.
Zhu et al. (2026) studied this question.