Studying at the University of Verona

Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.

A.A. 2014/2015

Academic calendar

The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.

Academic calendar

Course calendar

The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..

Definition of lesson periods
Period From To
primo semestre Sep 15, 2014 Jan 9, 2015
secondo semestre Feb 19, 2015 May 29, 2015
Exam sessions
Session From To
sessione invernale Jan 12, 2015 Feb 18, 2015
sessione estiva Jun 4, 2015 Jul 11, 2015
sessione autunnale Aug 24, 2015 Sep 9, 2015
Degree sessions
Session From To
sessione autunnale Dec 12, 2014 Dec 19, 2014
sessione invernale Apr 8, 2015 Apr 10, 2015
sessione estiva Sep 10, 2015 Sep 11, 2015
Holidays
Period From To
festività natalizie Dec 22, 2014 Jan 5, 2015
festività pasquali Apr 3, 2015 Apr 7, 2015
vacanze estive Aug 10, 2015 Aug 22, 2015

Exam calendar

Exam dates and rounds are managed by the relevant Economics Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.

Exam calendar

Should you have any doubts or questions, please check the Enrolment FAQs

Academic staff

B C D F G L M N P R V

Borello Giuliana

giuliana.borello@univr.it 045 802 8273

Bottiglia Roberto

roberto.bottiglia@univr.it 045 802 8224

Carluccio Emanuele Maria

emanuelemaria.carluccio@univr.it 045 802 8487

Centanni Silvia

silvia.centanni@univr.it 045 8425460

De Mari Michele

michele.demari@univr.it 045 802 8226

Frigo Paolo

paolo.frigo@univr.it

Grossi Luigi

luigi.grossi@univr.it 045 802 8247

Lubian Diego

diego.lubian@univr.it 045 802 8419

Mariani Francesca

francesca.mariani@univr.it 045 8028736

Minozzo Marco

marco.minozzo@univr.it 045 802 8234

Pichler Flavio

flavio.pichler@univr.it 045 802 8273

Rossi Francesco

francesco.rossi@univr.it 045 8028067

Rutigliano Michele

michele.rutigliano@univr.it 0458028610

Vaona Andrea

andrea.vaona@univr.it 045 8028537

Study Plan

The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University. Please select your Study Plan based on your enrolment year.

CURRICULUM TIPO:
ModulesCreditsTAFSSD
9
B
(SECS-P/11)
6
B
(SECS-P/01)
9
B
(SECS-S/06)
9
B
(SECS-S/06)
ModulesCreditsTAFSSD
6
B
(SECS-P/11)
9
C
(SECS-S/06)
6
F
(-)

1° Year

ModulesCreditsTAFSSD
9
B
(SECS-P/11)
6
B
(SECS-P/01)
9
B
(SECS-S/06)
9
B
(SECS-S/06)

2° Year

ModulesCreditsTAFSSD
6
B
(SECS-P/11)
9
C
(SECS-S/06)
6
F
(-)
Modules Credits TAF SSD

Legend | Type of training activity (TTA)

TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.




SPlacements in companies, public or private institutions and professional associations

Teaching code

4S02482

Coordinatore

Marco Minozzo

Credits

9

Scientific Disciplinary Sector (SSD)

SECS-S/01 - STATISTICS

Language

Italian

Period

primo semestre dal Sep 15, 2014 al Jan 9, 2015.

Learning outcomes

The course provides to students in economics and finance an overview of the theory of probability at an intermediate level.
Prerequisite to the course is an elementary knowledge of probability at the level of an undergraduate first or second year introductory course in probability and statistics.
In particular, a basic knowledge of the following topics is recommended: most common univariate discrete and continuous distributions; weak law of large numbers; central limit theorem.
The final objective of the course is to give an introduction to the advanced theory of conditional expectation, of stochastic processes in the discrete and continuous time domains and to stochastic integration.

Program

Probability spaces and Kolmogorov’s axioms: sigma-algebras; event trees; elementary conditional probability; Bayes theorem; independence.

Random variables: discrete, absolutely continuous and singular random variables; expectation; Tchebycheff inequality; Jensen inequality; moment generating function.

Multidimensional random variables: multidimensional discrete and continuous random variables; joint distribution function; joint density function; marginal and conditional distributions; marginal and conditional densities; independence; covariance; coefficient of correlation of Bravais; Cauchy-Schwarz inequality; joint moment generating function.

Distributions of functions of random variables: transformations of random variables; method of the distribution function; distribution of the minimum and the maximum; method of the moment generating function; log-normal distribution; probability integral transform; transformations of vectors of random variables.

Limits of random variables: infinite series of random variables; convergence in probability, in distribution, with probability one (almost surely) and in mean; weak law of large numbers and law of large numbers of Bernoulli for relative frequencies; central limit theorem; Borel’s lemma and Borel’s strong law of large numbers; order statistics; empirical distribution function.

Conditional expectation: conditional probability and conditional expectation with respect to a finite partition; conditional expectation with respect to a sigma-algebra.

Discrete time martingales: filtrations; martingales on finite probability spaces; martingales and stopping times; betting strategies and impossibility of a winning betting strategy.

Continuous time stochastic processes: definitions and finite-dimensional distributions; filtrations; adapted processes; filtrations generated by a stochastic process; stationary processes; processes with stationary increments and with independent increments; counting processes and Poisson processes; Gaussian processes and Wiener processes (Brownian motions); Wiener process as a limit of a random walk; properties and irregularities of the sample trajectories (non derivability and infinite variation); Markov processes, transition probabilities and Chapman-Kolmogorov equations; continuous time martingales.

Stochastic integrals: overview of Riemann-Stiltjes integral; definition and properties of Itô’s integral; Itô’s formula, properties and applications; martingales associated to a Wiener process; diffusions; geometric Brownian motion; Radom-Nikodym derivative; Girsanov's theorem.


The course consists of a series of lectures (54 hours).
All classes are essential to a proper understanding of the topics of the course.
The working language is Italian.

Bibliografia

Reference texts
Author Title Publishing house Year ISBN Notes
W. Feller An Introduction to Probability Theory and Its Applications, Volume 1 (Edizione 3) Wiley 1968
S. Lipschutz Calcolo delle Probabilità, Collana Schaum ETAS Libri 1975
P. Baldi Calcolo delle Probabilità e Statistica (Edizione 2) Mc Graw-Hill 1998 8838607370
T. Mikosch Elementary Stochastic Calculus With Finance in View World Scientific, Singapore 1999
R. V. Hogg, A. T. Craig Introduction to Mathematical Statistics (Edizione 5) Macmillan 1994
D. M. Cifarelli Introduzione al Calcolo delle Probabilità McGraw-Hill, Milano 1998
A. M. Mood, F. A. Graybill, D. C. Boes Introduzione alla Statistica McGraw-Hill, Milano 1991
G. R. Grimmett, D. R. Stirzaker One Thousand Exercises in Probability Oxford University Press 2001 0198572212
A. N. Shiryaev Probability (Edizione 2) Springer, New York 1996
G. R. Grimmett, D. R. Stirzaker Probability and Random Processes (Edizione 3) Oxford University Press 2001 0198572220
J. Jacod, P. Protter Probability Essentials Springer, New York 2000
S. E. Shreve Stochastic Calculus for Finance II: Continuous-Time Models Springer, New York 2004
S. E. Shreve Stochastic Calculus for Finance I: The Binomial Asset Pricing Model Springer, New York 2004
B. V. Gnedenko Teoria della Probabilità Editori Riuniti Roma 1979

Examination Methods

For the official examination both written and oral sessions are mandatory.
The course is considered completed if the candidate has done the written test and passed the oral exam.
Students that has received at least 15 out of 30 in the written exam are allowed to attend the oral exam.

Teaching materials

Type D and Type F activities

Modules not yet included

Career prospects


Module/Programme news

News for students

There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details.

Gestione carriere


Internships


Graduation

List of theses and work experience proposals

theses proposals Research area
Tesi di laurea magistrale - Tecniche e problemi aperti nel credit scoring Statistics - Foundational and philosophical topics
Il metodo Monte Carlo per la valutazione di opzioni americane Various topics

Linguistic training CLA


Further services

I servizi e le attività di orientamento sono pensati per fornire alle future matricole gli strumenti e le informazioni che consentano loro di compiere una scelta consapevole del corso di studi universitario.