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 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
I semestre Oct 1, 2019 Jan 31, 2020
II semestre Mar 2, 2020 Jun 12, 2020
Exam sessions
Session From To
Sessione invernale d'esame Feb 3, 2020 Feb 28, 2020
Sessione estiva d'esame Jun 15, 2020 Jul 31, 2020
Sessione autunnale d'esame Sep 1, 2020 Sep 30, 2020
Degree sessions
Session From To
Sessione di laurea estiva Jul 22, 2020 Jul 22, 2020
Sessione di laurea autunnale Oct 14, 2020 Oct 14, 2020
Sessione di laurea invernale Mar 16, 2021 Mar 16, 2021
Holidays
Period From To
Festa di Ognissanti Nov 1, 2019 Nov 1, 2019
Festa dell'Immacolata Dec 8, 2019 Dec 8, 2019
Vacanze di Natale Dec 23, 2019 Jan 6, 2020
Vacanze di Pasqua Apr 10, 2020 Apr 14, 2020
Festa della Liberazione Apr 25, 2020 Apr 25, 2020
Festa del lavoro May 1, 2020 May 1, 2020
Festa del Santo Patrono May 21, 2020 May 21, 2020
Festa della Repubblica Jun 2, 2020 Jun 2, 2020
Vacanze estive Aug 10, 2020 Aug 23, 2020

Exam calendar

Exam dates and rounds are managed by the relevant Science and Engineering 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 Enrollment FAQs

Academic staff

A B C D G L M O R S Z

Albi Giacomo

symbol email giacomo.albi@univr.it symbol phone-number +39 045 802 7913

Albiero Andrea

symbol email andrea.albiero@univr.it

Angeleri Lidia

symbol email lidia.angeleri@univr.it symbol phone-number +39 045 802 7911

Baldo Sisto

symbol email sisto.baldo@univr.it symbol phone-number +39 045 802 7935

Bos Leonard Peter

symbol email leonardpeter.bos@univr.it

Boscaini Maurizio

symbol email maurizio.boscaini@univr.it

Busato Federico

symbol email federico.busato@univr.it

Caliari Marco

symbol email marco.caliari@univr.it symbol phone-number +39 045 802 7904

Castellini Alberto

symbol email alberto.castellini@univr.it symbol phone-number +39 045 802 7908
Foto,  March 10, 2017

Cordoni Francesco Giuseppe

symbol email francescogiuseppe.cordoni@univr.it

Dai Pra Paolo

symbol email paolo.daipra@univr.it symbol phone-number +39 045 802 7093

Daldosso Nicola

symbol email nicola.daldosso@univr.it symbol phone-number +39 045 8027076 - 7828 (laboratorio)

Di Persio Luca

symbol email luca.dipersio@univr.it symbol phone-number +39 045 802 7968

Gonzato Guido

symbol email guido.gonzato@univr.it symbol phone-number 045 802 8303

Gregorio Enrico

symbol email Enrico.Gregorio@univr.it symbol phone-number +39 045 802 7937

Laking Rosanna Davison

symbol email rosanna.laking@univr.it symbol phone-number +39 045 802 7838

Liptak Zsuzsanna

symbol email zsuzsanna.liptak@univr.it symbol phone-number +39 045 802 7032

Mantese Francesca

symbol email francesca.mantese@univr.it symbol phone-number +39 045 802 7978

Marigonda Antonio

symbol email antonio.marigonda@univr.it symbol phone-number +39 045 802 7809

Mazzuoccolo Giuseppe

symbol email giuseppe.mazzuoccolo@univr.it symbol phone-number +39 0458027838

Migliorini Sara

symbol email sara.migliorini@univr.it symbol phone-number +39 045 802 7908

Monti Francesca

symbol email francesca.monti@univr.it symbol phone-number +39 045 802 7910

Orlandi Giandomenico

symbol email giandomenico.orlandi at univr.it symbol phone-number +39 045 802 7986

Rizzi Romeo

symbol email romeo.rizzi@univr.it symbol phone-number +39 045 802 7088

Sansonetto Nicola

symbol email nicola.sansonetto@univr.it symbol phone-number +39 045 802 7932

Schiavi Simona

symbol email simona.schiavi@univr.it symbol phone-number +39 045 802 7803

Schuster Peter Michael

symbol email peter.schuster@univr.it symbol phone-number +39 045 802 7029

Solitro Ugo

symbol email ugo.solitro@univr.it symbol phone-number +39 045 802 7977

Zivcovich Franco

symbol email franco.zivcovich@univr.it

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 enrollment year.

CURRICULUM TIPO:

1° Year 

ModulesCreditsTAFSSD

2° Year   activated in the A.Y. 2020/2021

ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
activated in the A.Y. 2020/2021
ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°
1 module between the following
Between the years: 1°- 2°
1 module between the following
Between the years: 1°- 2°
Between the years: 1°- 2°
Other activities
4
F
-

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.




S Placements in companies, public or private institutions and professional associations

Teaching code

4S001109

Coordinator

Luca Di Persio

Credits

6

Language

English en

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

Period

I semestre dal Oct 1, 2019 al Jan 31, 2020.

Learning outcomes

The Mathematical Finance course for the internationalized Master's Degree ( completely taught in English) aims to introduce the main concepts of discrete as well as continuous time, stochastic approach to the theory of modern financial markets. In particular, the fundamental purpose of the course is to provide the mathematical tools characterizing the setting of Itȏ stochastic calculus for the determination, the study and the analysis of models for options, interest rates models, financial derivatives, etc., determined by stochastic differential equations driven by Brownian motion and/or impulsive random noises. Basic ingredients are the foundation of the theory of continuous-time martingale, Girsanov theorems and the Feynman–Kac theorem and their applications to the theory of option pricing with specific examples in equities, also considering path-dependent options, and within the framework of interest rates models. Great attention will be also given to the practical study and realisation of concrete models characterising the modern approach to both the risk managment and option pricing frameworks, also by mean of numerical computations and computer oriented lessons. It is important to emphasize how the Stochastic Systems course is organized in such a way that students can concretely complete and further develop their own: °ability to establish profound connections with non-mathematical disciplines, both in terms of motivation of mathematical research and of the application of the results of such surveys; ° capacity of analysis, synthesis and abstraction; ° specific computational and computer skills; ° ability to understand texts, even advanced, of Mathematics in general and Applied Mathematics in particular; • ability to develop mathematical models for physical and natural sciences, while being able to analyze its limits and actual applicability, even from a computational point of view; ° skills concerning how to develop mathematical and statistical models for the economy and financial markets; ° capacity to extract qualitative information from quantitative data; ° knowledge of programming languages or specific software.

Program

[1] Stochastic analysis: basics

Basics on stochastic processes
Stochastic processes: main examples in discrete and continuous time
Stochastic integration
The Itô-Döblin lemma
SDEs: basics with examples ( e.g.: the linear case, multiplicative noise case)
Solution of SDEs as Markov processes
Feynman-Kac formula
Girsanov theorem
Stochastic control: basics with examples (e.g.: dynamic programming principle, Pontryagin maximum principle)

[2] Discrete time models
Contingent claims, value process, hedging strategies, completeness, arbitrage
Fundamental theorems of Asset Pricing (in discrete time)
Binomial trees
Random walk and pricing
Black and Scholes formula ( derived by binomial trees analysis )


[3] Brownian Motion (BM)
review of the main properties of the BM: filtration generated by BM, martingale property, quadratic variation, volatility, reflection properties, etc.

[4] Continuous time models
Black-Scholes-Merton Equation
Evolution of Portfolio/Option Values
Sensitivity analysis
The Martingale approach
Hedging and replicating strategies
Equity market models
Siegel paradox
Packages and Exotic options


[5] Interest rates models
Markovian Models of the Short Rate
Merton model
Stochastic interest rate for the Black and Scholes model
Hedging portfolio
Change of numeraire ( also under multiple risk sources )
Caps, floors, collars
Interest rates models
Vasicek model
Cox-Ingersoll-Ross model
Forward rates modelling
Arbitrage models for term structure
Heath-Jarrow-Morton framework
The Hull-White extended Vasicek model

[6] Portfolio choice and Asset Pricing
Bachelier and Samuelson models
Utility functions
The Merton problem ( value and static programming approach)
Utility maximization problem

[7] Miscellanea
Valuation of Options in Gaussian Models
Forward LIBORs
Swap rates modelling
Mean Field Games approach to systems of interacting financial agents
Calibration for Interest Rate models
Stochastic control and financial models (e.g.: the Heston model case)
Stochastic volatility models and applications
Polynomial/asyntotic espansions for financial models
SDEs on networks with financial applications

Reference texts
Author Title Publishing house Year ISBN Notes
I. Karatzas and S. Shreve Brownian motion and stochastic calculus  
R. Cont, P. Tankov Financial Modelling With Jump Processes Chapman and Hall, CRC Press 2003
D. Lamberton and B. Lapeyre Introduction to Stochastic Calculus Applied to Finance  
A. F. McNeil, R. Frey, P. Embrechts Quantitative Risk Management:Concepts, Techniques and Tools Princeton University Press 2015
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

Examination Methods

Oral exam with written exercise:
the exam is based on open questions as well as on the resolution of written exercises to be solved during the test itself. Questions, open-ended and exercises, aim at verify both the knowledge about arguments developed within the course, the solution of concrete problems belonging to Mathematical Finance, and to the acquired acquaintance of associated tools of stochastic analysis.

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE

Type D and Type F activities

I semestre From 10/1/19 To 1/31/20
years Modules TAF Teacher
1° 2° Python programming language D Maurizio Boscaini (Coordinator)
1° 2° SageMath F Zsuzsanna Liptak (Coordinator)
1° 2° History of Modern Physics 2 D Francesca Monti (Coordinator)
1° 2° History and Didactics of Geology D Guido Gonzato (Coordinator)
II semestre From 3/2/20 To 6/12/20
years Modules TAF Teacher
1° 2° Advanced topics in financial engineering D Luca Di Persio (Coordinator)
1° 2° C Programming Language D Sara Migliorini (Coordinator)
1° 2° C++ Programming Language D Federico Busato (Coordinator)
1° 2° LaTeX Language D Enrico Gregorio (Coordinator)
List of courses with unassigned period
years Modules TAF Teacher
1° 2° Axiomatic set theory for mathematical practice F Peter Michael Schuster (Coordinator)
1° 2° Corso Europrogettazione D Not yet assigned
1° 2° Corso online ARPM bootcamp F Not yet assigned
1° 2° ECMI modelling week F Not yet assigned
1° 2° ESA Summer of code in space (SOCIS) F Not yet assigned
1° 2° Google summer of code (GSOC) F Not yet assigned
1° 2° Higher Categories - Seminar course F Lidia Angeleri (Coordinator)

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 also via the Univr app.

Alternative learning activities

In order to make the study path more flexible, it is possible to request the substitution of some modules with others of the same course of study in Mathematics at the University of Verona (if the educational objectives of the modules to be substituted have already been achieved in the previous career), or with others of the course of study in Mathematics at the University of Trento.

Documents


Attendance modes and venues

As stated in the Teaching Regulations , except for specific practical or lab activities, attendance is not mandatory. Regarding these activities, please see the web page of each module for information on the number of hours that must be attended on-site.

Part-time enrolment is permitted. Find out more on the Part-time enrolment possibilities page.

The course's teaching activities take place in the Science and Engineering area, which consists of the buildings of Ca‘ Vignal 1, Ca’ Vignal 2, Ca' Vignal 3 and Piramide, located in the Borgo Roma campus. 
Lectures are held in the classrooms of Ca‘ Vignal 1, Ca’ Vignal 2 and Ca' Vignal 3, while practical exercises take place in the teaching laboratories dedicated to the various activities.


Career management


Student login and resources


Graduation

Deadlines and administrative fulfilments

For deadlines, administrative fulfilments and notices on graduation sessions, please refer to the Graduation Sessions - Science and Engineering service.

Need to activate a thesis internship

For thesis-related internships, it is not always necessary to activate an internship through the Internship Office. For further information, please consult the dedicated document, which can be found in the 'Documents' section of the Internships and work orientation - Science e Engineering service.

Final examination regulations

Upon completion of the Master’s degree dissertation students are awarded 32 CFU. The final examination consists of a written dissertation on a specific topic agreed with a supervising professor and presented to a commission (Dissertation Committee).

The dissertation can be high-level theoretical or experimental (in the latter case, it may focus on either basic or applied research), it can deal with a theoretical topic or propose the resolution of a specific problem, or description of a work project, and may be carried out at universities, research institutions, schools, laboratories and companies in the framework of internships, traineeships, study stays in Italy and abroad. The dissertation must be original and written by the student under the guidance of a Supervisor. At the request of the student, the dissertation may be written and presented in Italian.

Professors belonging to the Mathematics Teaching Committee, the Department of Computer Science, and any associated departments may be appointed as Supervisors, as well as any professors from the University of Verona whose area of interest (SSD - Scientific-disciplinary Sector) is included in the teaching regulations of the degree programme.

Students may take the final exam only if meeting all requirements set by the School of Sciences and Engineering.

The Master's degree in Mathematics is obtained by successfully passing the final examination and thus earning the 120 CFU included in the study plan.

The material submitted by the student for the final examination will be examined by the Dissertation Committee, which comprises three professors, possibly including the Supervisor, and appointed by the President of the Teaching Committee. The final examination will be assessed based on the following criteria: the student’s performance during the entire study programme, the knowledge acquired during the dissertation work, their understanding of the topic and autonomy of judgment, their ability to apply such knowledge, and communicate effectively and fully all the outcomes of the work and the main results obtained.

The final examination and the degree ceremony will be carried out, in one of the four graduation sessions throughout the academic year, by the Final Examination Committee appointed by the President of the Teaching Committee, and made up of a president and at least four members chosen from among the professors of the University.

For further information, please refer to the Final examination regulations.

Documents

Title Info File
File pdf 1. Come scrivere una tesi pdf, it, 31 KB, 02/11/22
File pdf 2. How to write a thesis pdf, en, 31 KB, 02/11/22
File pdf 5. Regolamento tesi pdf, it, 171 KB, 20/03/24

List of thesis proposals

theses proposals Research area
Controllo di sistemi multiagente Calculus of variations and optimal control; optimization - Hamilton-Jacobi theories, including dynamic programming
Controllo di sistemi multiagente Calculus of variations and optimal control; optimization - Manifolds
Controllo di sistemi multiagente Calculus of variations and optimal control; optimization - Optimality conditions
Formule di rappresentazione per gradienti generalizzati Mathematics - Analysis
Formule di rappresentazione per gradienti generalizzati Mathematics - Mathematics
Mathematics Bachelor and Master thesis titles Various topics

Erasmus+ and other experiences abroad