2020/2021

2020/2021

DM270

MAT/06 (PROBABILITÀ E STATISTICA MATEMATICA)

DIPARTIMENTO DI SCIENZE ECONOMICHE E AZIENDALI

ECONOMICS, FINANCE AND INTERNATIONAL INTEGRATION - ECONOMIA, FINANZA E INTEGRAZIONE INTERNAZIONALE

Finance

1°

Primo Semestre (28/09/2020 - 22/12/2020)

9

66 ore di attività frontale

English

SCRITTO

FERRARIO BENEDETTA (titolare) - 9 CFU

The course requires basic knowledge of Probability typically taught in an introductory course in Probability and Statistics. In particular, we assume the Student knows the following concepts: discrete and continuous random variables, expectation and variance, conditional probability, law of large numbers, central limit theorem.

This is a course on Probability and Stochastic Processes, having economic and financial applications in view. Accordingly, after introducing some basic notions of probability theory (including conditional expectation), lectures will focus on those processes which are popular in finance, including martingales, submartingales and Brownian motion. As far as possible, technicalities are avoided. Various exercises will be discussed as well.

- Random variables and vectors
- Distribution functions
- Transformations of random variables and vectors
- Filtrations
- Conditional expectation
- Martingales, sub- and super-martingales
- Stopping times
- Brownian motion
- Poisson process
- Ito integral
- stochastic differential equations

Because of the Covid-19 emergency, the lessons will be taught partially as face-to-face teaching but distance teaching will be guaranteed. Details will be communicated to Students in the due time, according to the evolution of the health situation (see Kiro web page).

* Brzezniak Z. and Zastawniak T. (1999). "Basic Stochastic Processes". Springer.
* Grimmett G. and Stirzaker D. (2001-third edition). "Probability and random processes". Oxford.
Further notes will be provided during the course.

Written exam. The Student will be asked to solve exercises and give some theoretical result (definitions, properties and some proofs are required).

More details in Kiro's webpage.