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 |
|---|---|---|
| I semestre | Oct 1, 2019 | Jan 31, 2020 |
| II semestre | Mar 2, 2020 | Jun 12, 2020 |
| 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 |
| 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 |
| 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.
Should you have any doubts or questions, please check the Enrolment FAQs
Academic staff
+39 045 802 7913
maurizio.boscaini@univr.it
federico.busato@univr.it
Cordoni Francesco Giuseppe
francescogiuseppe.cordoni@univr.it
rosanna.laking@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 enrolment year.
| Modules | Credits | TAF | SSD |
|---|
1° 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.
Advanced topics in financial engineering (2019/2020)
Teaching code
4S009132
Academic staff
Coordinatore
Credits
6
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/06 - PROBABILITY AND STATISTICS
Period
II semestre dal Mar 2, 2020 al Jun 12, 2020.
Learning outcomes
The aim of the course, fully delivered in flipped-classroom mode, is to introduce students to the foundations of the modern theory of financial mathematics, with specific reference to the study of concrete models, currently used by major banking institutions, of market risk analysis, and insurance.
Program
Introduction
Notation
Linear algebra primer
Vector spaces
Linear transformations
Spectral decomposition
Metric and normed spaces
Inner product spaces
Matrix transpose-square-root
Matrix operations
Calculus
Differentiation
Numerical derivatives
Taylor expansion
Integration
Monotone functions
Convexity
Week 1
Introduction
About the ARPM Lab
About quantitative finance: P and Q
The "Checklist": executive summary
The Checklist: Step 1 - Risk drivers identification
Risk drivers identification
Equities
Fixed-income
Derivatives
Credit
Applications
Case studies - Checklist: summary
Step 1. Risk drivers identification - Historical
Step 1. Risk drivers identification - Monte Carlo
Week 2
The Checklist: Step 2 - Quest for invariance (univariate)
Quest for invariance
Simple tests
Efficiency: random walk
Mean-reversion (continuous state): ARMA
Mean-reversion (discrete state)
Volatility clustering
Distributions
Representations of a distribution
Normal distribution
Notable multivariate distributions
Elliptical distributions
Scenario-probability distributions
Exponential family distributions
Mixture distributions
Applications
Step 2. Quest for invariance - Historical
Step 2. Quest for invariance - Monte Carlo
Week 3
Location and dispersion
Expectation and variance
Expectation and covariance
L2 geometry
Generalized location-dispersion: variational principles
Copulas
Univariate results
Definition and properties of copulas
The Checklist: Step 2 - Quest for invariance (multivariate)
Order-one autoregression
Cointegration
The Checklist: Step 3 - Estimation
Estimation
Setting the flexible probabilities
Historical
Maximum likelihood
Robustness
Applications
Step 3. Estimation - Historical
Step 3. Estimation - Monte Carlo
Week 4
Linear factor models
Factor models and learning
Overview
Regression LFM's
Principal component LFM's
Factor-analysis LFM's
Cross-sectional LFM's
Application: principal component analysis of the yield curve
Week 5
Machine learning: foundations and prediction
Overview
Point vs. probabilistic statements
Inference and learning
Least squares regression
Week 6
Bias reduction
Quantile and non-least-squares regression
Applications
Machine learning for hedging: introduction
Machine learning for hedging: least squares regression
Machine learning for hedging: least absolute distance regression
Week 7
Machine learning: foundations and prediction
Classification
Least squares autoencoders
Probabilistic graphical models
Week 8
Machine learning: out of sample enhancements
Estimation risk assessment
Regularization and features selection
Bayesian estimation
Ensemble learning
Credit default classification
Dynamic models
Overview
Linear state space models
Spectral representation
Probabilistic state space models
Week 9
The Checklist: Step 4 - Projection
Projection
One-step historical projection
Monte Carlo
Historical
The Checklist: Step 5 - Pricing at the horizon
Pricing at the horizon
Exact repricing
Taylor approximations
Applications
Step 4. Projection - Historical
Step 4. Projection - Monte Carlo
Step 5. Pricing at the horizon - Historical
Step 5. Pricing at the horizon - Monte Carlo
Week 10
The Checklist: Step 6 - Aggregation
Aggregation
Returns
Static market/credit risk
Enterprise risk management
The Checklist: Step 7 - Ex-ante evaluation
Ex-ante evaluation
Stochastic dominance
Satisfaction/risk measures
Mean-variance trade-off
Expected utility and certainty-equivalent
Quantile (value at risk)
Spectral satisfaction measures/Distortion expectations
Applications
Step 6. Aggregation - Historical
Step 6. Aggregation - Monte Carlo
Step 7. Ex-ante evaluation - Historical
Step 7. Ex-ante evaluation - Monte Carlo
Week 11
The Checklist: Step 8a - Ex-ante attribution: performance
Ex-ante attribution: performance
Bottom-up exposures
Top-down exposures: factors on demand
The Checklist: Step 8b - Ex-ante attribution: risk
Risk budgeting: general criteria
Homogenous measures and Euler decomposition
Applications
Step 8. Ex-ante attribution - Historical
Step 8. Ex-ante attribution - Monte Carlo
Week 12
The Checklist: Step 9a - Construction: portfolio optimization
Construction: portfolio optimization - Overview
Mean-variance principles
Analytical solutions of the mean-variance problem
Continuous programming
Integer N-choose-K heuristics
Mean-variance pitfalls
The Checklist: Step 10 - Execution
Execution
High frequency risk drivers
Market impact modeling
Order scheduling
Applications
Step 9. Construction - Historical
Step 9. Construction - Monte Carlo
Step 10. Execution - Historical
Step 10. Execution - Monte Carlo
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| A. F. McNeil, R. Frey, P. Embrechts | Quantitative Risk Management:Concepts, Techniques and Tools | Princeton University Press | 2015 | ||
| Ngai Hang Chan, Hoi Ying Wong | Simulation Techniques in Financial Risk Management (Edizione 1) | Wiley | 2015 | 9781118735817 | |
| S. E. Shreve | Stochastic Calculus for Finance II: Continuous-Time Models | Springer, New York | 2004 |
Examination Methods
The exam will consist in the presentation of a project, an in-depth study of one of the founding themes of the entire course, with particular reference to stochastic models for calculating risk. Furthermore, using the flipped-classroom mode, students will be asked to carry out weekly exercises relating to the individual topics covered during the lessons, so that the final grade will be expressed by mediating between the results obtained in solving these weekly exercises, and the grade obtained post presentation of the aforementioned project.
Type D and Type F activities
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° 2° | Python programming language | D |
Maurizio Boscaini
(Coordinatore)
|
| 1° 2° | SageMath | F |
Zsuzsanna Liptak
(Coordinatore)
|
| 1° 2° | History of Modern Physics 2 | D |
Francesca Monti
(Coordinatore)
|
| 1° 2° | History and Didactics of Geology | D |
Guido Gonzato
(Coordinatore)
|
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° 2° | Advanced topics in financial engineering | D |
Luca Di Persio
(Coordinatore)
|
| 1° 2° | C Programming Language | D |
Sara Migliorini
(Coordinatore)
|
| 1° 2° | C++ Programming Language | D |
Federico Busato
(Coordinatore)
|
| 1° 2° | LaTeX Language | D |
Enrico Gregorio
(Coordinatore)
|
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° 2° | Axiomatic set theory for mathematical practice | F |
Peter Michael Schuster
(Coordinatore)
|
| 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
(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.
Erasmus+ and other experiences abroad
Double degree
The University of Verona, through a network of agreements with foreign universities, offers international courses that enable students to gain a Double/Joint degree at the time of graduation. Indeed, students enrolled in a Double/Joint degree programme will be able to obtain both the degree of the University of Verona and the degree issued by the Partner University abroad - where they are expected to attend part of the programme -, in the time it normally takes to gain a common Master’s degree. The institutions concerned shall ensure that both degrees are recognised in the two countries.
Places on these programmes are limited, and admissions and any applicable grants are subject to applicants being selected in a specific Call for applications.
The latest Call for applications for Double/Joint Degrees at the University of Verona is available now!
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.Attachments
| Title | Info File |
|---|---|
1. Convenzione | Learning Agreement UNITN - UNIVR
|
167 KB, 27/08/21 |
|
2. Sostituzione insegnamenti a UNITN - Courses replacement at UNITN
|
44 KB, 30/08/21 |
|
3. Sostituzione insegnamenti a UNIVR - Courses replacement at UNIVR
|
113 KB, 30/08/21 |
Attendance
As stated in the Teaching Regulations for the A.Y. 2022/2023, 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.
Please refer to the Crisis Unit's latest updates for the mode of teaching.
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.
Attachments
| Title | Info File |
|---|---|
|
1. Come scrivere una tesi
|
31 KB, 02/11/22 |
|
2. How to write a thesis
|
31 KB, 02/11/22 |
|
5. Regolamento tesi (valido da luglio 2022)
|
171 KB, 02/11/22 |
List of theses and work experience 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 |
| Stage | Research area |
|---|---|
| Internship proposals for students in mathematics | Various topics |
