Debt and the Optimal Incentives Over Time

Oct 3, 2025

Zhaohui Chen , Juraj Foldes

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Using a backward stochastic differential equation (BSDE) framework, we examine the principal-agent problem in a finite-horizon continuous-time setting where the agent’s effort is a continuous choice, and the principal can impose non-pecuniary punishments. We show that the agent’s optimal incentive scheme, dependent on time and the firm’s state, can be implemented by the principal holding a standard or callable debt, and the agent owns the firm. The agent always exerts a positive effort. Furthermore, optimally reducing the debt burden when the firm’s value falls below a critical threshold aligns with practices such as repricing executive options to maintain incentives. Our results highlight debt contracts as adaptable tools for dynamic incentive alignment.

Zhaohui Chen

Zhaohui Chen

University of Virginia

Juraj Foldes

Juraj Foldes