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.
Academic calendar
The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technicaladministrative 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.
Course calendar
The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..
Period  From  To 

primo semestre magistrali  Sep 30, 2019  Dec 20, 2019 
secondo semestre magistrali  Feb 24, 2020  May 29, 2020 
Session  From  To 

Sessione invernale magistrali  Jan 7, 2020  Feb 21, 2020 
Sessione estiva magistrali  Jun 3, 2020  Jul 10, 2020 
Autumn Session exams  Aug 24, 2020  Sep 11, 2020 
Session  From  To 

Autumn Session  Dec 2, 2019  Dec 4, 2019 
Winter Session  Apr 7, 2020  Apr 9, 2020 
Summer session  Sep 7, 2020  Sep 9, 2020 
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.
Academic staff
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.
Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

1° Year
Modules  Credits  TAF  SSD 

2° Year activated in the A.Y. 2020/2021
Modules  Credits  TAF  SSD 

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.
Stochastic Models for Finance (2019/2020)
Teaching code
4S02482
Academic staff
Coordinatore
Credits
9
Language
Italian
Scientific Disciplinary Sector (SSD)
SECSS/01  STATISTICS
Period
primo semestre magistrali dal Sep 30, 2019 al Dec 20, 2019.
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: sigmaalgebras; event trees; elementary conditional probability; Bayes theorem; independence.
• Random variables: discrete, absolutely continuous and singular random variables; expectation; Chebyshev 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; CauchySchwarz 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; lognormal 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 sigmaalgebra.
• 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 finitedimensional 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 ChapmanKolmogorov equations; continuous time martingales.
• Stochastic integrals: overview of RiemannStiltjes integral; definition and properties of Itô’s integral; Itô’s formula, properties and applications; martingales associated to a Wiener process; diffusions; geometric Brownian motion; RadomNikodym derivative; Girsanov's theorem.
TEXTBOOKS
 A. M. Mood, F. A. Graybill, D. C. Boes (1991). Introduzione alla Statistica. McGrawHill, 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: ContinuousTime Models. Springer, New York.
 S. E. Shreve (2004). Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. Springer, New York.
SUPPORTING MATERIAL
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 Elearning platform of the University.
READING LIST
 P. Baldi (2011). Calcolo delle Probabilità, 2a Edizione. Mc GrawHill, Milano.
 D. M. Cifarelli (1998). Introduzione al Calcolo delle Probabilità. Mc GrawHill, 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 (1991). Probability and Random Processes, Solved Problems, 2nd Edition. The Claredon Press, Oxford University Press.
 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.
STUDY GUIDE
Detailed indications, regarding the use of the textbooks, will be given during the course.
PREREQUISITES
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
Exercises are an integral part of the course and are necessary to an adequate understanding of the topics.
TEACHING METHODS
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.
TUTORING ACTIVITIES
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.
Author  Title  Publishing house  Year  ISBN  Notes 

W. Feller  An Introduction to Probability Theory and Its Applications, Volume 1 (Edizione 3)  Wiley  1968  
P. Baldi  Calcolo delle Probabilità (Edizione 2)  McGrawHill  2011  9788838666957  
S. Lipschutz  Calcolo delle Probabilità, Collana Schaum  ETAS Libri  1975  
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  McGrawHill, Milano  1998  
A. M. Mood, F. A. Graybill, D. C. Boes  Introduzione alla Statistica  McGrawHill, 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  
G. R. Grimmett, D. R. Stirzaker  Probability and Random Processes: Solved Problems (Edizione 2)  The Clarendon Press, Oxford University Press, New York  1991  
J. Jacod, P. Protter  Probability Essentials  Springer, New York  2000  
G. Casella, R. L. Berger  Statistical Inference (Edizione 2)  Duxbury Thompson Learning  2002  
S. E. Shreve  Stochastic Calculus for Finance II: ContinuousTime 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 e documents
 01) Informazioni sul corso (pdf, it, 86 KB, 20/09/19)
Type D and Type F activities
years  Modules  TAF  Teacher  

2°  Simulation and Implementation of Economic Policies  D 
Federico Perali
(Coordinatore)


1° 2°  Enactus Verona 2020  D 
Paola Signori
(Coordinatore)


1° 2°  Parlare in pubblico e economic writing  D 
Martina Menon
(Coordinatore)


1° 2°  Samsung Innovation Camp  D 
Marco Minozzo
(Coordinatore)

years  Modules  TAF  Teacher  

2°  Simulation and Implementation of Economic Policies  D 
Federico Perali
(Coordinatore)


1° 2°  Predictive analytics for business decisions  2019/20  D 
Claudio Zoli
(Coordinatore)


1° 2°  Professional communication for economics  2019/20  D 
Claudio Zoli
(Coordinatore)


1° 2°  Parlare in pubblico e economic writing  D 
Martina Menon
(Coordinatore)


1° 2°  Regulation, procurement and competition  2019/20  D 
Claudio Zoli
(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: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and soon also via the Univr app.
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 
Fattori ESG e valutazione d'azienda  Various topics 
Il metodo Monte Carlo per la valutazione di opzioni americane  Various topics 
Il Minimum Requirement for own funds and Eligible Liabilities (MREL)  Various topics 
L'acquisto di azioni proprie  Various topics 
Proposte Tesi A. Gnoatto  Various topics 