Optimal Executive Compensation when Firm Size Follows Geometric Brownian Motion

This paper studies a continuous-time agency model in which the agent controls the drift of the geometric Brownian motion firm size. The changing firm size generates partial incentives, analogous to awarding the agent equity shares according to her continuation payoff. When the agent is as patient as investors, performance-based stock grants implement the optimal contract. Our model generates a leverage effect on the equity returns, and implies that the agency problem is more severe for smaller firms. That the empirical evidence shows that grants compensation are largely based on the CEO's historical performance—rather than current performance—lends support to our model.