Debt and the Optimal Incentives Over Time
Oct 3, 2025
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.