A Game Theoretic approach to Time Inconsistent Stochastic Control

In this thesis we want to study a specific type of stochastic control problems that have the characteristic of being time inconsistent, namely they do not allow for a Bellman's optimality principle. In this context, the very concept of optimality becomes problematic, since a strategy which is optimal given a specific starting point in time and space may be non-optimal when viewed from a later date and different state. We will attack this general class of problems using a game-theoretic approach, so instead of looking for optimal strategies, we will search for subgame perfect Nash equilibrium strategies: this procedure will bring us to state and prove a Verification Theorem. In the end, we will provide some examples and applications.