Tesis Doctorado
Contributions to the Principal-Agent theory and applications in economics
Contribuciones a la teoría de Agente-Principal y aplicaciones en economía
Autor
Hernández-Santibáñez, Nicolás Iván
Institución
Resumen
In this thesis, theoretical aspects and applications in economics of the Principal-Agent model are studied. The first part of the thesis presents two applications of the model. In the first one, an electricity provider determines the optimal tariff of consumption for its clients. Population is heterogeneous and the provider observes perfectly the consumption of the clients. This leads to a setting of adverse selection without moral hazard. The problem of the Principal writes as a non-standard variational problem, which can be solved under certain particular forms of the reservation utility of the population. The optimal contracts obtained are either linear or polynomial with respect to the consumption and the electricity provider contracts only consumers with either low or high appetite for electricity. In the second application, a bank monitors a pool of identical loans subject to Markovian contagion. The bank raises funds from an investor, who cannot observe the actions of the bank and neither knows his ability to do the job. This is an extension of the model of Pagès and Possamaï (2013) to the case of both moral hazard and adverse selection. Following the approach of Cvitanić, Wan and Yang (2009) to these problems, the dynamic credible set is computed explicitly and the value function of the investor is obtained through a recursive system of variational inequalities. The properties of the optimal contracts are discussed in detail. In the second part of the thesis, the problem of an Agent controlling the drift of a diffusion process under volatility uncertainty is studied. It is assumed that the Principal and the Agent have a worst–case approach to the problem and they act as if a third player, the Nature, was choosing the worst possible volatility. This work is an extension to Mastrolia and Possamaï (2015) and Sung (2015) to a more general framework. It is proved that the value function of the agent can be represented as the solution to a second–order BSDE, and also that the value function of the Principal corresponds to the unique viscosity solution of the associated Hamilton-Jacobi-Bellman-Isaacs equation, given that the latter satisfies a comparison result. PFCHA-Becas PFCHA-Becas