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 26, 2016  Jan 13, 2017 
Secondo Semestre Magistrali  Feb 27, 2017  Jun 1, 2017 
Session  From  To 

Appelli esami sessione invernale  Jan 16, 2017  Feb 17, 2017 
Appelli esami sessione estiva  Jun 5, 2017  Jul 7, 2017 
Appelli esami sessione autunnale  Aug 28, 2017  Sep 15, 2017 
Session  From  To 

Sessione autunnale  Nov 30, 2016  Dec 1, 2016 
Sessione invernale  Apr 5, 2017  Apr 7, 2017 
Sessione estiva  Sep 11, 2017  Sep 13, 2017 
Period  From  To 

Vacanze natalizie  Dec 23, 2016  Jan 5, 2017 
Vacanze pasquali  Apr 14, 2017  Apr 18, 2017 
Vacanze estive  Aug 7, 2017  Aug 25, 2017 
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.
Should you have any doubts or questions, please check the Enrolment FAQs
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
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 (2016/2017)
Teaching code
4S02482
Academic staff
Coordinatore
Credits
9
Language
Italian
Scientific Disciplinary Sector (SSD)
SECSS/01  STATISTICS
Period
Primo semestre Magistrali dal Sep 26, 2016 al Jan 13, 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.
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; 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; 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.
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.
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 GrawHill  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  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  
J. Jacod, P. Protter  Probability Essentials  Springer, New York  2000  
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
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.
Bibliography
Teaching materials
 01) Informazioni sul corso (pdf, it, 542 KB, 27/09/16)
Type D and Type F activities
years  Modules  TAF  Teacher  

1°  Programming in Matlab  D  Not yet assigned  
1°  Programming in SAS  D  Not yet assigned  
1°  Programming Stata (3 cfu)  D  Not yet assigned  
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.
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.
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 