Dynamic contracting with imperfect observability

Title: Dynamic contracting with imperfect observability (with Ben Goldys, University of Sydney)

Abstract: This paper is concerned with a continuous time, dynamic contracting problem in which the principal observes performance at discrete intervals only. In spite of this, incentive compatibility can always be enforced pathwise, but at a cost.  The discrete nature of the information of the principal gives rise to a mixed problem with continuous and impulse controls that is characterised by a quasi-variational inequality.  We show the value function is smooth and concave and fully characterise the contract, which includes continuous and discrete payments that can be computed explicitly.  In equilibrium, the agent may quit unexpectedly, and the principal may overpay or pay too late; these are the informational costs.