Optimal Share-Based Payments

We investigate the design of optimal share-based incentive contracts by formulating a stochastic differential game between a listed company and a representative manager. The value maximizing company can grant share-based payments to the manager as incentive component of the total salary package at a premium. The manager is assumed to maximize utility from investment and consumption net of the cost for work effort. The information asymmetry is built into the model by allowing the manager to observe the level of share-based payments granted by the company. The effort exercised by the manager and her investment and consumption decision cannot be observed by the company. Accordingly we obtain a stochastic differential game of Stackelberg type. For this setting we identify a Stackelberg equilibrium that is subgame perfect Nash equilibrium by construction. Based on the equilibrium strategies we derive the optimal contract design. The results are discussed emphasizing the effect of company characteristics such as volatility and size, and manager characteristics, such as work productivity