B0324 - EQUAZIONI DIFFERENZIALI STOCASTICHE I

Learning outcomes

At the end of the course the student knows Ito's stochastic calculus, the fundamental notions of stochastic differential equations theory, and the relationship with the theory of partial differential equations of elliptic and parabolic type. In particular, she is able to study independently mathematical disciplines that need the knowledge of stochastic analysis. 

Course contents

We will present the theory of stochastic differential equations, of stochastic optimal control, and their relationship with partial differential equations of elliptic and parabolic type.

In particular, we will deal with the following topics:

• Recalls of stochastic calculus: Ito's formula, stochastic integration theory
  
• Stochastic differential equations: existence of strong solutions, uniqueness in law, Markov property, Lp estimations and dependence on the initial data
• Martingale representation theorem
• Formula di Feynman-Kac: relationship between stochastic differential equations and the theory of partial differential equations
• Stochastic optimal control: problem formulation, dynamic programming principle, verification theorem
• Girsanov theorem
• Backward stochastic differential equations: existence and uniqueness, nonlinear Feynman-Kac formula

Readings/Bibliography

Paolo Baldi, Equazioni differenziali stocastiche ed applicazioni, Pitagora Editrice, Bologna 2000.

 

Huyen Pham, Continuous-time Stochastic Control and Optimization with Financial Applications, Springer 2010.

Teaching methods

Traditional lectures concerning both theory and exercises. 

Assessment methods

Final oral exam verifying the ability to deal with theory and exercises. 

Teaching tools

Web site of the course on the platform virtuale.unibo.it where one can find: notes of the course, list of exercises, and other useful informations. 

Office hours

See the website of Elena Bandini

See the website of Cristina Di Girolami