PROBABILITY AND STOCHASTIC PROCESSES
Stampa
Anno immatricolazione
2020/2021
Anno offerta
2020/2021
Normativa
DM270
SSD
MAT/06 (PROBABILITÃ€ 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
Anno di corso
Periodo didattico
Primo Semestre (28/09/2020 - 22/12/2020)
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, submartingales 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, sub- and super-martingales
- Stopping times
- Brownian motion
- Poisson process
- Ito integral
- stochastic differential equations
Metodi didattici
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).
Testi di riferimento
* 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.
Modalità verifica apprendimento
Written exam. The Student will be asked to solve exercises and give some theoretical result (definitions, properties and some proofs are required).
Altre informazioni
More details in Kiro's webpage.
Obiettivi Agenda 2030 per lo sviluppo sostenibile