The role of boundary solutions in principal–agent problems of the Holmström–Milgrom type

The paper extends the Holmström–Milgrom [B. Holmström, P. Milgrom, Aggregation and linearity in the provision of intertemporal incentives, Econometrica 55 (1987) 303–328] analysis of intertemporal incentive provision to allow for the implementation of actions on the boundary of the feasible set. Boundary actions provide the principal with some freedom in choosing incentive schemes. This can be used to reduce premia. The paper characterizes optimal incentive schemes for the continuous-time Brownian-motion model and its discrete-time approximations. Linearity of incentive schemes in “accounts” is confirmed. However, for models with effort costs depending only on mean returns, the availability of boundary actions destroys the linearity of optimal incentive schemes in profits.