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.
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 |
|---|---|---|
| Semester 1 | Oct 2, 2023 | Jan 26, 2024 |
| Semester 2 | Mar 4, 2024 | Jun 14, 2024 |
| Session | From | To |
|---|---|---|
| Winter exam session | Jan 29, 2024 | Mar 1, 2024 |
| Summer exam session | Jun 17, 2024 | Jul 31, 2024 |
| Autumn exam session | Sep 2, 2024 | Sep 30, 2024 |
| Session | From | To |
|---|---|---|
| Summer graduation session | Jul 22, 2024 | Jul 22, 2024 |
| Autumn graduation session | Oct 22, 2024 | Oct 22, 2024 |
| Winter graduation session | Mar 27, 2025 | Mar 27, 2025 |
| Period | From | To |
|---|---|---|
| Festa di Ognissanti | Nov 1, 2023 | Nov 1, 2023 |
| Festa dell'Immacolata | Dec 8, 2023 | Dec 8, 2023 |
| Vacanze di Natale | Dec 24, 2023 | Jan 7, 2024 |
| Festività pasquali | Mar 29, 2024 | Apr 1, 2024 |
| Ponte della Festa della Liberazione | Apr 25, 2024 | Apr 26, 2024 |
| Festa del Lavoro | May 1, 2024 | May 1, 2024 |
| Festività del Santo Patrono: San Zeno | May 21, 2024 | May 21, 2024 |
| Festa della Repubblica | Jun 2, 2024 | Jun 2, 2024 |
| Vacanze estive | Aug 12, 2024 | Aug 17, 2024 |
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.
Should you have any doubts or questions, please check the Enrollment FAQs
Academic staff
+39 045 802 7913
andrea.albiero@univr.it
mila.dallapreda@univr.it
giulio.fellin@univr.it
elena.gaburro@univr.it
alessia.mandini@univr.it
ramon.oliverbonafoux@univr.it
claudio.tomazzoli@univr.it
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.
1° Year
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
|---|
1 module among the following 1 module between the following (a.a. 2023/24 Homological Algebra not activated - a.a. 2024/25 Computational Algebra not activated)3 modules among the followingLegend | 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.
Mathematical finance (2023/2024)
Teaching code
4S001109
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/06 - PROBABILITY AND STATISTICS
Period
Semester 1 dal Oct 2, 2023 al Jan 26, 2024.
Courses Single
Authorized
Learning objectives
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.
Prerequisites and basic notions
Basic probability theory tools. Basic knowledge of the theory of stochastic processes. Preferential: knowledge of the rudiments of stochastic calculus.
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
Bibliography
Didactic methods
Lectures with sharing of teaching material via slides, lecture notes, scientific articles and specific bibliographic references to deepen particular subjects and (optional) developing ongoing projects.
Learning assessment procedures
Oral exam with written exercises:
the exam is based on open questions as well as on the resolution of written exercises to be solved during the test itself
and/or on questions and exercises based on specific projects presented during the exam and previously agreed with the professor. 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.
Evaluation criteria
Evaluation of the understanding of mathematical tools, with particular reference to the theory of stochastic calculus, necessary for the rigorous definition of the main models of modern mathematical finance.
Criteria for the composition of the final grade
The final grade is the result of the evaluation of the final oral exam, with the possible inclusion of the ongoing assessments relating to projects (optional) carried out by the student .
Exam language
Inglese / English
Sustainable Development Goals - SDGs
This initiative contributes to the achievement of the Sustainable Development Goals of the UN Agenda 2030. More information on sustainability
Type D and Type F activities
Type D learning activities are the student's choice, type F activities are additional knowledge useful for job placement (internships, transversal skills, project works, etc.). According to the Teaching Regulations of the Course, some activities can be chosen and entered independently in the booklet, others must be approved by a special committee to verify their consistency with the study plan. Type D or F learning activities can be covered by the following activities.
1. Modules taught at the University of Verona
Include the modules listed below and/or in the Course Catalogue (which can also be filtered by language of delivery via Advanced Search).
Booklet entry mode: if the teaching is included among those listed below, the student can enter it independently during the period in which the curriculum is open; otherwise, the student must make a request to the Secretariat, sending the form to carriere.scienze@ateneo.univr.it during the period indicated.
2. CLA certificate or language equivalency
In addition to those required by the curriculum/study plan, the following are recognized for those matriculated from A.Y. 2021/2022:
- English language: 3 CFUs are recognized for each level of proficiency above that required by the course of study (if not already recognized in the previous course of study).
- Other languages and Italian for foreigners: 3 CFUs are recognized for each proficiency level starting from A2 (if not already recognized in the previous study cycle).
These CFUs will be recognized, up to a maximum of 6 CFUs in total, of type F if the study plan allows it, or of type D. Additional elective credits for language knowledge may be recognized only if consistent with the student's educational project and if adequately justified.
Those enrolled until A.Y. 2020/2021 should consult the information found here.
Method of inclusion in the booklet: request the certificate or equivalency from CLA and send it to the Student Secretariat - Careers for the inclusion of the exam in the career, by email: carriere.scienze@ateneo.univr.it
3. Transversal skills
Discover the training paths promoted by the University's TALC - Teaching and learning center intended for students regularly enrolled in the academic year of course delivery https://talc.univr.it/it/competenze-trasversali
Mode of inclusion in the booklet: the teaching is not expected to be included in the curriculum. Only upon obtaining the Open Badge will the booklet CFUs be automatically validated. The registration of CFUs in career is not instantaneous, but there will be some technical time to wait.
4. CONTAMINATION LAB
The Contamination Lab Verona (CLab Verona) is an experiential course with modules on innovation and enterprise culture that offers the opportunity to work in teams with students from all areas to solve challenges set by companies and organisations.
Upon completion of a CLab, students will be entitled to receive 6 CFU (D- or F-type credits).
Find out more: https://www.univr.it/clabverona
PLEASE NOTE: In order to be admitted to any teaching activities, including those of your choice, you must be enrolled in the academic year in which the activities in question are offered. Students who are about to graduate in the December and April sessions are therefore advised NOT to undertake extracurricular activities in the new academic year in which they are not enrolled, as these graduation sessions are valid for students enrolled in the previous academic year. Therefore, students who undertake an activity in an academic year in which they are not enrolled will not be granted CFU credits.
5. Internship/internship period
In addition to the CFUs stipulated in the curriculum/study plan (check carefully what is indicated on the Teaching Regulations): here information on how to activate the internship.
Check in the regulations which activities can be Type D and which can be Type F.
Modules and other activities that can be entered independently in the booklet
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° 2° | Introduction to quantum mechanics for quantum computing | D |
Claudia Daffara
(Coordinator)
|
| 1° 2° | Introduction to Robotics for students of scientific courses. | D |
Andrea Calanca
(Coordinator)
|
| 1° 2° | Mathematics mini courses |
Giacomo Albi
(Coordinator)
|
|
| 1° 2° | Web and mobile app design using react and react native | D |
Graziano Pravadelli
(Coordinator)
|
| 1° 2° | Firmware development with bluetooth low energy (BLE) protocol and freertos operating system | D |
Franco Fummi
(Coordinator)
|
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° 2° | Introduction to Robotics for students of scientific courses. | D |
Andrea Calanca
(Coordinator)
|
| 1° 2° | Python programming language | D |
Carlo Combi
(Coordinator)
|
| 1° 2° | Mathematics mini courses |
Giacomo Albi
(Coordinator)
|
|
| 1° 2° | Programming Challanges | D |
Romeo Rizzi
(Coordinator)
|
| 1° 2° | Protection of intangible assets (SW and invention)between industrial law and copyright | D |
Mila Dalla Preda
(Coordinator)
|
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° 2° | Cooperative Game Theory in the (Deep) RL Era | D |
Alessandro Farinelli
(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
| Title | Info File |
|---|---|
1. Convenzione | Learning Agreement UNITN - UNIVR
|
pdf, it, 167 KB, 27/08/21 |
|
2. Sostituzione insegnamenti a UNITN - Courses replacement at UNITN
|
pdf, it, 97 KB, 29/07/24 |
|
3. Sostituzione insegnamenti a UNIVR - Courses replacement at UNIVR
|
pdf, it, 113 KB, 30/08/21 |
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 |
|---|---|
|
1. Come scrivere una tesi
|
pdf, it, 31 KB, 02/11/22 |
|
2. How to write a thesis
|
pdf, en, 31 KB, 02/11/22 |
|
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 |
