Teaching code

4S008953

Teacher

Sara Svaluto-Ferro

Coordinator

Sara Svaluto-Ferro

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Period

Secondo semestre L dal Feb 16, 2026 al May 29, 2026.

Courses Single

Authorized

Lessons timetable Moodle Seminars 0

Learning objectives

The course aims to provide knowledge of basic quantitative tools and classic mathematical models for the analysis and evaluation of the main economic-financial operations, of the financing contracts and investment projects, tools and models that can be used for an efficient business management. At the end of the lessons, the student must be able to correctly represent an economic and financial problem in a mathematical model, evaluating it so it takes into account the right hypotheses, the correct choice of the mathematical expressions and the correct methodology for solving the problem; therefore, the teaching aims to develop the capacity for autonomous reasoning in the analysis and interpretation of concrete problems.

Prerequisites and basic notions

The course requires only a basic knowledge of elementary mathematics and statistics. It is strongly recommended, though not mandatory, to have previously taken courses in general mathematics and statistics.

Program

The course consists of 48 hours of lecture in addition to tutoring hours. The course material is available online by accessing the course web page. Although there are no formal prerequisites, for a profitable learning is recommended to pass at least the examinations of mathematics and statistics. The proposed content will be structured as follows.
1. Financial regimes. Financial operations, regime of simple interest, of capitalization several times a year, of compound interest. Financial arbitrage, splitting of financial laws, spot rates, forward rates.
2. Non-elementary financial transactions. Annuities and amortization, present value and upside, net present value (NPV), implicit rate (IRR), NPV and APR, amortization schedules, common forms of amortization, investment returns, selection criteria for investments and loans.
3. Bonds. Classification of bonds, bonds without coupons, bonds with fixed coupons, estimation of term structure of rates. Control/immunization of/from interest rate risk: duration and convexity.
4. Portfolio selection. Investments in assets with random returns. Expected return and volatility/risk of a portfolio of assets. Risk aversion and the Markowitz model.

Bibliography

Learning assessment procedures

**General guidelines**
The examination aims at verifying the deepening of the themes developed in the course, in particular the ability to perform operations with the tools provided by the course and the ability to critically analyze theoretical concepts.
The mode of verification of learning consists of a written test.
The written test (duration: 2h) assesses the ability to:
- solve financial mathematics exercises
- explain the essential steps of the procedure in a clear manner;
- answer questions, both theoretical and practical, in a brief and precise manner;
• The result of the written test is published with the score assigned to each exercise.
• The written test is allowed the use of a form prepared by the teacher; the use of any other form of material is expressly forbidden;
• During the written test the use of a scientific calculator is allowed (and necessary); the use of any other electronic instrument is expressly forbidden.
During the tests the use of a form provided by the teacher and a calculator is allowed. It is not possible to consult other material or use computer equipment (PC, tablet, smartphone, smartwatch,...), otherwise the exam will be invalidated.
There is an intermediate test with grade that can be used as a partial exemption to the exam, as explained in the course presentation.

Evaluation criteria

The examination aims at verifying the deepening of the themes developed in the course, in particular the ability to perform operations with the tools provided by the course and the ability to critically analyze theoretical concepts.

Criteria for the composition of the final grade

The final grade coincides with the overall score obtained in the exam and is expressed on a 30-point scale. This score is determined by the final written exam and, if taken and passed, by the midterm exam.
The midterm exam is optional and awards a maximum of 15 points. Students who obtain at least 7.5 points in the midterm exam are exempt from answering questions on the topics covered by the midterm exam in the final written exam; for these students, the final exam lasts one hour and awards a maximum of 15 points. In this case, the overall score—and therefore the final grade—is given by the sum of the score obtained in the midterm exam and the score obtained in the final written exam, up to a maximum of 30 points.
Students who do not take the midterm exam, who do not achieve the minimum score of 7.5 points, or who choose to reject the midterm grade must take the full final written exam, which lasts two hours and awards a maximum of 30 points. In this case as well, the score obtained in the final written exam coincides with the final grade.

Exam language

Italiano