Understand and formulate control problems governed by ordinary or stochastic differential equations.

Define and interpret the value function and its role in optimal control.

Analyze optimal control problems using both Pontryagin’s Maximum Principle and Dynamic Programming.

Analyze and solve the Linear Quadratic Regulator (LQR) problem in both deterministic and stochastic settings.

Formulate and solve Merton’s optimal investment problem as a classical example of stochastic control in finance.

Understand and analyze optimal stopping problems, including applications in finance such as the pricing of American options.