Abstract:

This paper provides a complete review of the continuous--time optimal contracting problem introduced by Sannikov (2008) in the extended context allowing for possible different discount factors of both parties. The agent's problem is to seek for optimal effort, given the compensation scheme proposed by the principal over a random horizon. Then, given the optimal agent's response, the principal determines the best compensation scheme in terms of running payment, retirement, and lump--sum payment at retirement. 
A Golden parachute is a situation where the agent ceases any efforts at some positive stopping time, and receives a payment afterwards, possibly consisting of a lump sum and/or 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. Namely, we show that there is no Golden Parachute if this parameter is too large. Similarly, in the context of a concave marginal utility, there is no Golden Parachute if the agent's utility function has a too negative curvature 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, 2008) continuous's solution). In particular, different discount factors induce naturally a {\it face-lifted utility function}, which allows to reduce the whole analysis to the equal-discount factors setting. Finally, we also confirm that an agent with small reservation utility does have an informational rent, meaning that the principal optimally offers him a contract with strictly higher utility value.