Contracting with discretionary bonuses
Guillermo Alonso Alvarez, Ibrahim Ekren, Liwei Huang
TL;DR
This paper develops a finite-horizon, continuous-time principal–agent model with endogenized bonus timing, casting the interaction as a mixed control and stopping problem. It combines BSDE representations for the agent with a viscosity-solution framework for the principal’s recursive control problem, deriving bounds in the first-best and a rigorous solution structure in the second-best. Numerical experiments reveal that the first-best value dominates the second-best and that discretionary bonuses generally outperform fixed schedules; signing bonuses (golden hello) appear in some impatience regimes but shrink as the number of bonuses grows. The work provides a principled explanation for dynamic bonus design and staking of incentives in time, with clear implications for how patience, risk aversion, and horizon length shape optimal contract features.
Abstract
We study a continuous time contracting model in which a principal hires a risk averse agent to manage a project over a finite horizon and provides sequential payments whose timing is endogenously determined. The resulting nonzero-sum interaction between the principal and the agent is reformulated as a mixed control and stopping problem. Using numerical simulations, we investigate how factors such as the relative impatience of the parties and the number of bonus payments influence the principal's value and the structure of the optimal bonus payment scheme. A notable finding is that, in some contractual environments, the principal optimally offers a sign-on bonus to front-load incentives.