Stochastic Control and Games with Different Information Structures

We will start by giving a short introduction of the most important approaches for solving stochastic control problems and games based on partial differential equations and backward stochastic differential equations. In those problems an agent or a group of players are willing to optimize some objectives, which depend on the state of a controlled stochastic dynamic system. In this part, the latter will be assumed to be fully observable. Then, we will tackle the more realistic case where the agent/players have only a partial information on the state variable. Filtering theory will play a crucial role in this class of problems. After that, we will pass to the case when the agent/players can have different information structures on the state. Finally, we will consider some relevant applications in energy economics, Bayesian persuasion and finance. A good knowledge of the basis of stochastic calculus is required to fully understand the content of the course.