Appears in collection : Distributed Control: Decentralization and Incentives / Contrôle Distribué: Décentralisation et Incitations

These lectures will consist in an overview of recent progresses made in contracting theory, using the so-called dynamic programming approach. The basic situation is that of a Principal wanting to hire an Agent to do a task on his behalf, and who has to be properly incentivized. We will show how this general framework allows to treat volatility control problems arising for instance in delegated portfolio management, or in electricity pricing. If time permit, we will also analyze the situation of a Principal hiring a finite number of Agents who can interact with each other, as well as the associated mean-field problem. The theory will be mostly illustrated by examples ranging from finance and insurance applications to regulation issues.