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 [18], 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.
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 agent's 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 welfare's volatility on the optimal contract is studied.
This article studies the problem of evaluating the information that a Principal lacks when establishing an incentive contract with an Agent whose effort is not observable. The Principal ("she") pays a continuous rent to the Agent ("he"), while the latter gives a best response characterized by his effort, until a terminal date decided by the Principal when she stops the contract and gives compensation to the Agent. The output process of the project is a diffusion process driven by a Brownian motion whose drift is impacted by the Agent's effort. The first part of the paper investigates the optimal stochastic control problem when the Principal and the Agent share the same information. This situation, known as the first-best case, is solved by tackling the Lagrangian problem. In the second part, the Principal observes the output process but she may not observe the drift and the Brownian motion separately. This situation is known as the second-best case. We derive the best response of the Agent, then we solve the mixed optimal stopping/stochastic control problem of the Principal under a fixed probability and on the filtration generated by the Brownian motion, which is larger than the one generated by the output process (that corresponds to the information available for the Principal). Under some regularity conditions, the Principal value function is characterized by solving the associated Hamilton Jacobi Bellman Variational Inequality. At the optimum, we prove that the two filtrations coincide. Finally, we compute the value of the information for the Principal provided by the observation of the Agent's effort. It is defined as the difference between the principal value function in the first-best and second-best cases.
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