Optimal stopping contract for Public Private Partnerships under moral hazard

This paper studies optimal Public Private Partnerships contract between a public entity and a consortium, in continuous-time and with a continuous payment, with the possibility for the public to stop the contract. The public (she) pays a continuous rent to the consortium (he), while the latter gives a best response characterized by his effort. This effect impacts the drift of the social welfare, until a terminal date decided by the public when she stops the contract and gives compensation to the consortium. Usually, the public can not observe the effort done by the consortium, leading to a principal agents problem with moral hazard. We solve this optimal stochastic control with optimal stopping problem in this context of moral hazard. The public value function is characterized by the solution of an associated Hamilton Jacobi Bellman Variational Inequality. The public value function and the optimal effort and rent processes are computed numerically by using the Howard algorithm. In particular, the impact of the social welfares volatility on the optimal contract is studied.

Optimal Contract with Moral Hazard for Public Private Partnerships

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.