PROBABILITY
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Bibliography
- Delivery method
- Teaching methods
- Contacts/Info
The basic notions of probability given in the “Matematica per l'economia e la finanza” course
Written exam (theory and exercises). Oral exam optional.
This course deals with the basic notions of stochastic processes and stochastic differential equations with particular attention to their financial applications. At the end of the course students should have acquired a deep knowledge of the concepts of stochastic process and its properties, stochastic and differential calculus, asset price models. Student are expected to be able to describe the main topics treated in the course and to develop some abilities for the resolution of simple questions and exercises.
Conditional expected value.
Stochastic processes and martingales.
Ordinary differential equations and applications to economics/finance
Stochastic differential equations and financial applications.
Girsanov Theorem and equivalent martingale measure (nods).
Conditional expected value.
a. Basic notions
b. Finite state space
c. General state space
d. Properties of the conditional expected value
Stochastic processes and martingales.
a. Discrete time stochastic processes
b. Random walk
c. Martingales
d. Martingales and gambling
e. Martingales and investment strategies
f. Ruin and success probability
g. Continuous stochastic processes; Brownian motion
Ordinary differential equations and applications to economics/finance
a. Basic notions and examples: dynamics of a bank account; Solow’s growth model; production management
b. Existence and uniqueness of solutions
Stochastic differential equations and financial applications.
a. Stochastic integral
b. Stochastic differential and Ito formula
c. Examples: Dynamics of a risky asset; interest rate models
Girsanov Theorem and equivalent martingale measure (nods).
No textbook is officially adopted. Students' notes plus additional material posted by the instructor.
Students might want to have a look at:
Sheldon M. Ross - Stochastic Processes 2nd Edition, Wiley, 1996
A. Simon, K. Blume, Mathematics for economists
A. Guerraggio, S. Salsa (1997), Metodi matematici per l’economia e le scienze
sociali, (Giappichelli)
Class lectures
This course can be seen as a continuation of the Probability topics presented in the Matematica per l'Economia e la Finanza course.