### Social sciences and humanities

## Subject: FINANCIAL MATHEMATICS (A.A. 2024/2025)

### degree course in ECONOMICS AND FINANCE

Course year | 2 |
---|---|

CFU | 6 |

Teaching units |
Unit Matematica finanziaria
Statistics and Mathematics (lesson)
- TAF: Compulsory subjects, characteristic of the class SSD: SECS-S/06 CFU: 6
Silvia MUZZIOLI |

Exam type | written |

Evaluation | final vote |

Teaching language | Italiano |

### Teachers

### Overview

The aim of the course is provide the student with the basic notions of financial mathematics. Moreover, it will deepen the notions of calculus of several variables, quadratic forms, unconstrained optimization, provided in the first year.

For the financial mathematics part the course focuses on time value of money, annuities, loan repayment, capital budgeting, term structure of interest rates, bonds, interest rate risk.

For the objectives of the course see the section about the expected learning outcomes

### Admission requirements

basic notions of calculus (course of matematics and financial mathematics of the first year)

### Course contents

The timeline is purely indicative, it can be modified following students' feeddback.

Block 1 .3 CFU 21 hours

time value of money, annuities, loan repayment, capital budgeting, temporal indices, term structure of interest rates,

Block 2. 1 CFU 7 hours

bonds, interest rate measurement and management

Block 3. 2 CFU 14 hours

Calculus of several variables, quadratic forms,

unconstrained and constrained optimization.

### Teaching methods

Teaching is delivered through face-to-face lectures. Attendance at the course is not mandatory but strongly recommended. Each lecture is made of a theoretical part and a practical part (solution of exercises) with examples from the web. The teaching is delivered in Italian. Each lecture is video recorded. The video recordings are available on teams

### Assessment methods

Assessment method: the exam consists of a written exam. The exam will take place at the end of the course according to the official exam session calendar. The test is written. The duration is 1 hour. The exam consists of 8 closed multiple choice questions. Multiple-choice questions have four answer options each, only one of which is correct. The correct answer is awarded 1 point, the answer not given 0 and the wrong answer -0.5. These questions are aimed at assessing: - knowledge and understanding skills; - the application of knowledge and understanding; - autonomy of judgement. The rating scale is in thirtieths. The exam is passed with an overall score of at least 18/30. The test results will be communicated by insertion in esse3 within two weeks of the test. More informations are available at the web page: http://morespace.unimore.it/silviamuzzioli/mate-clef

### Learning outcomes

1) Knowledge and understanding

at the end of the course, it is hoped that the student will be able to:

Know and understand compound financial transactions, debt amortization, the criteria for choosing between investments and bonds.

Know and understand the free optimization of functions of several variables.

2) Applied knowledge and understanding:

Knowing how to represent and solve economic problems of free optimization. Knowing how to use financial valuation functions, investment selection criteria and bond valuation models in real problems.

3) Autonomy of judgment

a) verify one's degree of learning and understanding of the concepts exposed thanks to the possibility of intervention in the lesson and the possibility represented by the exercises;

b) reorganize the knowledge learned and implement one's own ability to critically and autonomously evaluate what has been learned.

4) Communication skills

a) correctly and logically express one's knowledge, recognizing the required topic and answering the exam questions in a timely and complete manner.

b) synthesize and fully elaborate the fundamental elements of general and financial mathematics illustrating the key concepts and the elements of distinction and internal connection.

5) Learning ability

a) deepen the notions learned to continue one's university career by making use of terminology, schemes, concepts as tools to achieve a 360-degree knowledge of financial applications;

b) mastering and refining one's own mathematical language, remembering its constitutive and expressive elements and learning to use the logical-mathematical method of reasoning.

### Readings

per la parte di analisi matematica:

-Simon C. P., Blume, L.E. (2002) Matematica 2 per l’Economia e le Scienze Sociali, Università Bocconi Editore, Milano. (SB)

per la parte di matematica finanziaria:

- Stefani S., Torriero A., Zambruno G. (2011), Elementi di matematica finanziaria e cenni di programmazione lineare, IV Edizione, Giappichelli Editore, Torino (STZ)

Eserciziari:

- Angoli A., Colli Franzone Bonzanini A., De Dionigi L., Matematica finanziaria e attuariale, Esercizi svolti, Giappichelli, Torino 2006.

-Bolamperti G., Ceccarossi G., Elementi di Matematica Finanziaria e cenni di programmazione lineare, Esercizi, Giappichelli Editore, Torino