  Public-Private Partnership (PPP) is a contract between a public entity and a
consortium, in which the public outsources the construction and the maintenance
of an equipment (hospital, university, prison...). One drawback of this
contract is that the public may not be able to observe the effort of the
consortium but only its impact on the social welfare of the project. We aim to
characterize the optimal contract for a PPP in this setting of asymmetric
information between the two parties. This leads to a stochastic control under
partial information and it is also related to principal-agent problems with
moral hazard. Considering a wider set of information for the public and using
martingale arguments in the spirit of Sannikov, the optimization problem can be
reduced to a standard stochastic control problem, that is solved numerically.
We then prove that for the optimal contract, the effort of the consortium is
explicitly characterized. In particular, it is shown that the optimal rent is
not a linear function of the effort, contrary to some models of the economic
literature on PPP contracts.
