Is there a Golden Parachute in Sannikov’s principal–agent problem?

Résumé

This paper provides a complete review of the continuous–time optimal contracting problem introduced by Sannikov [2008], in the extended context allowing for possibly different discount rates of both parties. A Golden Parachute is a situation where the agent ceases any effort at some positive stopping time, and receives a payment afterwards, possibly under the form of a lump sum payment, or of a continuous stream of payments. We show that a Golden Parachute only exists in certain specific circumstances. This is in contrast with the results claimed by Sannikov [2008], where the only requirement is a positive agent’s marginal cost of effort at zero. In the general case, we provide a rigorous analysis of this problem, and we prove that an agent with positive reservation utility is either never retired by the principal, or retired above some given threshold (as in Sannikov’s solution). In particular, different discount factors induce naturally a face–lifted utility function, which allows to reduce the whole analysis to a setting similar to the equal–discount rates one.