Managerial Limited Commitment: A New Class of Stochastic Control Problems

Ai and Li [2015] introduced a problem at the interface of the neoclassical investment and dynamic contract theories. Specifically, the authors consider the optimal design of a contract that provides sufficient incentives to the management for it to implement the shareholder’s investment plan despite the former’s limited commitment. This problem involves a participation constraint such that the management’s continuation value exceeds the value of an outside option. This constraint, which must be satisfied at any time in an economic environment prone to productivity shocks, leads to a new class of stochastic control problems. Our objective in this paper is to address the new technical challenges arising in such a class of problems and to construct the optimal policy and value function in case of a strictly convex adjustment cost function and contrast our results to those obtained by Ai and Li [2015] for the bang-bang control case.