# Mathematics for Economics and Finance (2017/2018)

### Course partially running (all years except the first)

Course code
4S02835
Name of lecturer
Francesco Rossi
Coordinator
Francesco Rossi
Number of ECTS credits allocated
6
MAT/09 - OPERATIONS RESEARCH
Language of instruction
Italian
Location
VERONA
Period
Primo Semestre Triennali dal Sep 18, 2017 al Jan 12, 2018.

#### Learning outcomes

The teaching 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
While there will be no formal prerequisites to make profitable learning, you should have already passed the exam of Mathematics, the first year, and of Statistics, in the second year.

#### Syllabus

Financial transactions: capitalization and discounting. Financial laws: upright, present value, interest, discount, interest rate and discount rate. Regime of simple interest, capitalization several times a year, compound, the discount trade. Interest rates equivalent to periods other than the year. Financial arbitrage, severability of financial laws, spot rate, forward rates. Force of interest. Currency transactions. Nominal interest rates, inflation, real interest rates.

2. Compound Financial transactions
Financial transactions and their classification. Current value and upright of a set of financial movements. Net present value (NPV or NPV). Evaluation of the installment, the number of installments, the implicit rate (IRR). Consumer credit, TAN and APR. Amortization schedules and closing conditions. Straight-capital basis, in equal installments on a straight interest paid in advance, with shares of accumulation. The pre-amortization. Early repayment of a mortgage. Rate mortgages indexed. Financial leasing. Savings plans.
Bonds and evaluation of the price of a bond, estimates of the term structure of interest rates. Control / hedging of interest rate risk: duration and convexity.
Criteria for choosing between operations / financial projects: NPV, IRR, TRM, WACC.

3. Select Portfolio with two risky assets
Recall of probability theory: the mean, variance, correlation. Investment in assets yielding haphazard. Expected return and volatility / risk of a portfolio of assets. Risk aversion and Markowitz model. Return and risk of a portfolio: a random and activities in return for a certain yield, two activities to yield uncertain, two activities to yield randomly and a certain return. Capital Allocation Line. Capital Market Line.

Textbooks
➢ G. Scandolo, Matematica Finanziaria, Amon, Padova, 2013 (for the chapters concerned by the themes of points of the program) and Matematica Finanziaria: esercizi, Amon, Padova, 2013.
➢ for the synthesis and theoretical exercises about steps 1 and 2 is recommended:
A. Basso, P. Pianca, Introduzione alla Matematica Finanziaria, Cedam, Padova, 2010.
➢ as in Step 3 can also be seen:
F. Rossi, F. Mantovani, Teoria del portafoglio (diversificazione degli investimenti e controllo del profilo rendimento-rischio), Monduzzi Publisher, 2010, pages 1-46 and 75-86.

Teaching material is available online by accessing the web page of the course.

The conduct of the lessons
The course consists of 48 hours of lectures. There are also the hours of tutoring.

 Author Title Publisher Year ISBN Note Basso A., Pianca P. Introduzione alla Matematica Finanziaria CEDAM 2010 Scandolo Giacomo Matematica Finanziaria Amon 2013 Scandolo Giacomo Matematica finanziaria - Esercizi Amon 2013

#### Assessment methods and criteria

There is no intermediate assessment test.
At the end of the lessons, a final two-hour written exam is scheduled. The final written test covers all the topics in the program, it is divided into several questions inspired by the examples presented in the classroom as well as those contained in the material available online. The student must be provided with a calculator and the formula sheet, available online, formula sheet that, of course, must not contain additional information, otherwise there will be exclusion from the test.
The tests are aimed at ascertaining:
- knowledge of the topics in the program
- the ability to apply methods and models to the various economic-financial problems

The Commission may request an oral integration aimed at verifying:
- the depth and breadth of the acquired knowledge;
- the property of language;
- the ability to connect knowledge in a systemic way.