B0320 - STOCHASTIC CALCULUS II

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

1. Notes of the teacher
2. H. Pham, Continuous-time Stochastic Control and Optimization with Financial Applications,  Springer-Verlag (2009).
3. 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