- Docente: Salvatore Federico
- Credits: 6
- SSD: MAT/06
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Feb 20, 2025 to May 29, 2025
Learning outcomes
At the end of the course, the student knows the fundamental ideas and tools of stochastic control theory in continuous time and its connections with the theory of parabolic and elliptic partial differential equations. The student can independently carry out further studies on stochastic dynamic optimization for a wide range of applications (Economics, Finance, Biology, Epidemiology, Engineering).
Course contents
Part I - Introduction to optimal control theory
Introduction to optimal control and dynamic optimization: Motivations and examples. Formulation of optimal control problems in continuous time. Basic ideas and results of the dynamic programming method in the deterministic setting.
Part II - Stochastic optimal control
Bellman's optimality principle; Hamilton-Jacobi-Bellman equations: classical and viscosity solutions; some regularity results for HJB equations; verification theorems and transversality conditions. Applications to portfolio optimization.
Part III - Optimal stopping and singular stochastic control
Dynamic to programming equation and verification theorems. Applications American options and to irreversible investment problems.
Readings/Bibliography
- Notes of the teacher
- H. Pham, Continuous-time Stochastic Control and Optimization with Financial Applications, Springer-Verlag (2009).
- J. Yong, X.Y. Zhou, Stochastic controls: Hamiltonian systems and HJB equations, Springer (1999).
Teaching methods
Frontal lectures
Assessment methods
Oral exam
Teaching tools
Virtuale
Office hours
See the website of Salvatore Federico