Università di Pavia - Offerta formativa

PROBABILITY AND STOCHASTIC PROCESSES

Anno immatricolazione

2018/2019

Anno offerta

2018/2019

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

1°

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

- 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.

* 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.