- Docente: Salvatore Federico
- Crediti formativi: 6
- SSD: MAT/06
- Lingua di insegnamento: Inglese
- Modalità didattica: Convenzionale - Lezioni in presenza
- Campus: Bologna
- Corso: Laurea Magistrale in Matematica (cod. 5827)
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dal 20/02/2025 al 29/05/2025
Conoscenze e abilità da conseguire
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).
Contenuti
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.
Testi/Bibliografia
- 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).
Metodi didattici
Lezioni frontali
Modalità di verifica e valutazione dell'apprendimento
Esame orale
Strumenti a supporto della didattica
Virtuale
Orario di ricevimento
Consulta il sito web di Salvatore Federico