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Contrat optimal pour les partenariats public-privé avec aléa moral : une approche de contrôle stochastique

Abstract : In this thesis, we are interested in the contract with moral hazard for public private partnerships (PPP). PPP is defined as a long-term contract between a private party and a public entity, for the construction and/or the management of an asset or public service, in which the consortium takes the risks and a responsibility to manage the project. The public undertakes to pay him a rent. However, the effort that the consortium does to improve the social value of the project is not observable by the public. It is a principal-agent problem with moral hazard, in which the principal is the public and the agent is the consortium. We assume that the public pays the consortium continuously and the effort of the consortium affects the drift of the social value of the project. We assume that the agent is risk averse and the public is risk-neutral. In chapter 2 of the thesis, we consider a perpetual contract between a public entity and a consortium. We characterize the optimal contract in this moral hazard framework. We use the strong formulation : we consider different filtrations corresponding to the different level of information as in the context of stochastic control under partial observation. In this approach, we use martingale methods and stochastic control techniques. In chapter 3, we consider a public-private partnership problem with a random horizon, in which the public has the possibility to stop the contract at a fixed or a random time and gives compensation to the consortium. We solve this optimal stochastic control with optimal stopping problem in this context of moral hazard. We use the weak approach, that is the agent changes the distribution of the social value of the project by changing the drift and this amounts to considering a new probability that depends on the effort of the consortium. In the chapter 4, we also consider the problem of public-private partnership with a random horizon but using the strong formulation. Then, we deal with the risk-sharing framework, we assume that the public and the consortium have the same information. We analyze numerically the value of information. Chapter 5 focuses on the existence of a solution of the Hamilton Jacobi-Bellman equation that appears in our theoretical study. Then, we detail the numerical results for the numerical resolution of a Hamilton Jacobi-Bellman equation and variational inequality as part of our numerical study.
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Submitted on : Tuesday, November 24, 2020 - 3:01:07 PM
Last modification on : Thursday, May 6, 2021 - 4:19:44 PM
Long-term archiving on: : Thursday, February 25, 2021 - 8:17:44 PM


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  • HAL Id : tel-03021830, version 1



Ishak Hajjej. Contrat optimal pour les partenariats public-privé avec aléa moral : une approche de contrôle stochastique. Optimisation et contrôle [math.OC]. Institut Polytechnique de Paris; École nationale d'ingénieurs de Tunis (Tunisie), 2020. Français. ⟨NNT : 2020IPPAG007⟩. ⟨tel-03021830⟩



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