The goal of the seminar is to cover several key aspects of the continuous-time theory of stochastic optimal control. We will discuss the dynamic programming principle, Hamilton-Jacobi-Bellman (HJB) equation, verification theorem, viscosity solutions, comparison principle, backward stochastic differential equations, and the martingale duality method.
Lernziel
The following topics will be discussed:
- Basic setup for controlled diffusions. - Dynamic programming principle, the Hamilton-Jacobi-Bellman (HJB) equation, the verification theorem. - Viscosity solutions for the HJB equation, comparison principle, uniqueness. - Backward stochastic differential equations (BSDE), nonlinear Feynman-Kac formulas, stochastic maximum principle. - Martingale duality method.
Literatur
We will follow the book "Continuous-time Stochastic Control and Optimization with Financial Applications" by Huyên Pham.
Voraussetzungen / Besonderes
Knowledge of stochastic analysis at the level of the course Brownian Motion and Stochastic Calculus.
Leistungskontrolle
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)