Stochastic Control and Optimization
The lecture covers the following topics:
Stochastic optimization problems
Optimal stopping, classical stochastic control, singular control, impulse control.
Stochastic analysis
Martingale theory, stochastic differential equations.
Classical stochastic control
Controlled stochastic differential equations, optimization criteria, martingale optimality principle, Bellman principle, Hamilton-Jacobi-Bellman equations, applications.
Viscosity solutions
Non-differentiable value functions, viscosity solutions via test functions, viscosity solutions via semijets, comparison theorems, Ishii’s lemma.
The stochastic Perron’s method
Comparison theorem, stochastic sub- and supersolutions, viscosity characterization of the value function.
Resources
- Lecture Notes: Stochastic Control and Optimization (in German)
- Slides: Examples of Stochastic Optimization Problems (in German)
- Slides: Stochastic Analysis (in German)
- Slides: Classical Stochastic Control — Problem Pormulation (in German)
- Slides: Martingale Optimality and the Bellman Principle (in German)
- Slides: The Hamilton-Jacobi-Bellman Equation (in German)
- Slides: Optimal Fishing Rate and the Merton Problem (in German)
- Slides: Definition of Viscosity Solutions (in German)
- Slides: Sub- and Superjets (in German)
- Slides: Uniqueness and Ishii’s Lemma (in German)
- Slides: The Comparison Principle (in German)
- Slides: Stochastic Supersolutions (in German)
- Slides: Stochastic Subsolutions (in German)
- Slides: The Viscosity Property of the Value Function (in German)