Università di Pavia - Offerta formativa

PROBABILITY AND STOCHASTIC PROCESSES

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

1°

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

- 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.

* 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