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. 2017/2018

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 Magistrali Oct 2, 2017 Dec 22, 2017
Secondo Semestre Magistrali Feb 26, 2018 May 25, 2018
Exam sessions
Session From To
Esami sessione invernale Magistrali Jan 8, 2018 Feb 23, 2018
Esami sessione estiva Magistrali May 28, 2018 Jul 6, 2018
Esami sessione autunnale 2018 Aug 27, 2018 Sep 14, 2018
Degree sessions
Session From To
Lauree sessione autunnale (validità a.a. 2016/17) Nov 27, 2017 Nov 28, 2017
Lauree sessione invernale (validità a.a. 2016/17) Apr 4, 2018 Apr 6, 2018
Lauree sessione estiva (validità a.a. 2017/18) Sep 10, 2018 Sep 11, 2018
Period From To
All Saints Day Nov 1, 2017 Nov 1, 2017
Festa Immacolata Concezione Dec 8, 2017 Dec 8, 2017
attività sospese (Natale) Dec 23, 2017 Jan 7, 2018
Easter break Mar 30, 2018 Apr 3, 2018
Liberation Day Apr 25, 2018 Apr 25, 2018
attività sospese (Festa dei lavoratori) Apr 30, 2018 Apr 30, 2018
Labour Day May 1, 2018 May 1, 2018
Festa Patronale May 21, 2018 May 21, 2018
attività sospese estive Aug 6, 2018 Aug 24, 2018

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


Bottiglia Roberto 045 802 8224

Campolmi Alessia 045 802 8071

Carluccio Emanuele Maria 045 802 8487

De Mari Michele 045 802 8226

Frigo Paolo

Gnoatto Alessandro 045 802 8537

Grossi Luigi 045 802 8247

Lubian Diego 045 802 8419

Minozzo Marco 045 802 8234

Noto Sergio 045 802 8008

Oliva Immacolata +39 0458028768

Pichler Flavio 045 802 8273

Renò Roberto 045 802 8526

Rutigliano Michele 0458028610

Scricciolo Catia 045 802 8341

Taschini Luca 045 802 8736

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.

Final exam

2° Year

Final exam
Modules Credits TAF SSD
Between the years: 1°- 2°

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



Marco Minozzo



Scientific Disciplinary Sector (SSD)





Primo Semestre Magistrali dal Oct 2, 2017 al Dec 22, 2017.

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.


• 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.


- A. M. Mood, F. A. Graybill, D. C. Boes (1991). Introduzione alla Statistica. McGraw-Hill, Milano.
- B. V. Gnedenko (1979). Teoria della Probabilità. Editori Riuniti, Roma.
- R. V. Hogg, A. T. Craig (1994). Introduction to Mathematical Statistics, 5th Edition. Macmillan.
- A. N. Shiryaev (1996). Probability, 2nd Edition. Springer, New York.
- S. E. Shreve (2004). Stochastic Calculus for Finance II: Continuous-Time Models. Springer, New York.
- S. E. Shreve (2004). Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. Springer, New York.


Other supporting material, written records of the lessons, handouts, exercises and past exam papers with solutions will be distributed during the course and will be made available on the E-learning platform of the University.


- P. Baldi (1998). Calcolo delle Probabilità e Statistica, 2a Edizione. Mc Graw-Hill.
- D. M. Cifarelli (1998). Introduzione al Calcolo delle Probabilità. Mc Graw-Hill, Milano.
- W. Feller (1968). An Introduction to Probability Theory and Its Applications, Volume 1, 3rd Edition. Wiley.
- B. V. Gnedenko (1979). Teoria della Probabilità. Editori Riuniti, Roma.
- G. R. Grimmett, D. R. Stirzaker (2001). Probability and Random Processes, 3rd Edition. Oxford University Press.
- G. R. Grimmett, D. R. Stirzaker (2001). One Thousand Exercises in Probability. Oxford University Press.
- J. Jacod, P. Protter (2000). Probability Essentials. Springer, New York.
- S. Lipschutz (1975). Calcolo delle Probabilità, Collana Schaum. ETAS Libri.
- T. Mikosch (1999). Elementary Stochastic Calculus With Finance in View. World Scientific, Singapore.


Detailed indications, regarding the use of the textbooks, will be given during the course.


Students are supposed to have acquired all notions and basic concepts usually taught in a first undergraduate university course in probability and statistics: main discrete and continuous univariate distributions, main limit theorems such as the weak law of large numbers and the central limit theorem.


Exercises are an integral part of the course and are necessary to an adequate understanding of the topics.


Course load is equal to 54 hours (equal to 9 ECTS). All classes are essential to a proper understanding of the topics of the course. The working language is Italian.


In addition to lessons and exercise hours, before each exam session there will be tutoring hours devoted to revision. More detailed information will be available during the course.


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

The final exam consists of a written test (of two hours and 30 minutes) followed by an oral session (of approximately 30 minutes). Both written and oral sessions are mandatory. For the written test, students can use a scientific calculator; any other material (books, notes, etc.) is forbidden. To be admitted to the oral session, students must receive at least 15 out of 30 in the written test. Contents, assessment methods and criteria are the same for all students and do not depend on the number of classes attended.

Teaching materials

Type D and Type F activities

List of courses with unassigned period
years Modules TAF Teacher
An Introduction to the History of Economics and Business Economics D Sergio Noto (Coordinatore)
Introduction to dynamic optimization with economic applications D Not yet assigned
1° 2° Python Laboratory D Marco Minozzo (Coordinatore)
1° 2° Advanced Excel Laboratory (Verona) D Marco Minozzo (Coordinatore)
1° 2° Excel Laboratory (Verona) D Marco Minozzo (Coordinatore)

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.



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

Gestione carriere

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.