2018/2019

2018/2019

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 (24/09/2018 - 21/12/2018)

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, Markov chains 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
- Stopping times
- Markov chains
- Brownian motion
- Poisson process

All lectures are displayed on the blackboard. Students are introduced to main theoretical concepts and results through a number of examples and illustrations that considerably ease the understanding of the subject.

* Billingsley P. (1995). "Probability and Measure". Wiley, 3rd Edition.
* Brzezniak Z. and Zastawniak T. (1999). "Basic Stochastic Processes". Springer.

Oral exam. The student will be asked to present the main results taught. Some proofs are required but the emphasis is mainly on exercises and examples, showing a deep understanding of the subject.

Oral exam. The student will be asked to present the main results taught. Some proofs are required but the emphasis is mainly on exercises and examples, showing a deep understanding of the subject.