PROBABILITY AND STOCHASTIC PROCESSES
Stampa
Anno immatricolazione
2018/2019
Anno offerta
2018/2019
Normativa
DM270
SSD
MAT/06 (PROBABILITÀ E STATISTICA MATEMATICA)
Dipartimento
DIPARTIMENTO DI SCIENZE ECONOMICHE E AZIENDALI
Corso di studio
ECONOMICS, FINANCE AND INTERNATIONAL INTEGRATION - ECONOMIA, FINANZA E INTEGRAZIONE INTERNAZIONALE
Curriculum
Finance
Corso di studio
Periodo didattico
Primo Semestre (24/09/2018 - 21/12/2018)
Crediti
9
Ore
66 ore di attività frontale
Lingua insegnamento
English
Tipo esame
SCRITTO
Docente
FERRARIO BENEDETTA (titolare) - 9 CFU
Prerequisiti
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.
Obiettivi formativi
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.
Programma e contenuti
- Random variables and vectors
- Distribution functions
- Transformations of random variables and vectors
- Filtrations
- Conditional expectation
- Martingales
- Stopping times
- Markov chains
- Brownian motion
- Poisson process
Metodi didattici
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.
Testi di riferimento
* Billingsley P. (1995). "Probability and Measure". Wiley, 3rd Edition.
* Brzezniak Z. and Zastawniak T. (1999). "Basic Stochastic Processes". Springer.
Modalità verifica apprendimento
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.
Altre informazioni
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.