# Mathematics for Economics and Finance (2019/2020)

### 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
First semester bachelor degree dal Sep 16, 2019 al Jan 10, 2020.

#### 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.

#### Syllabus

1. Recalls of Mathematics and Statistics
2. Laws and financial regimes. Financial transactions: capitalization and discounting. Financial laws: amount, current value, interest, discount, interest rate and discount rate. Simple interest regime, capitalization several times a year, compound interest, commercial discount. Equivalent interest rates on periods other than the year. Financial arbitrage, the splitting of financial laws, spot rates, forward rates. Force of interest. Foreign currency transactions. Nominal rates, inflation, real rates.
3. Composite financial transactions. Composite financial transactions and their classification. Present value and upside of a set of financial movements. Net present value (NPV or NPV). Evaluation of the installment, the number of installments, the implied rate (IRR or IRR). Consumer credit, TAN and TAEG. Depreciation plans and closing conditions. Depreciation to constant capital shares, in constant installments, in advance interest installments, with accumulation shares. The pre-depreciation. Early repayment of a mortgage. Indexed rate mortgages. Financial leasing. Accumulation plans.
Bond loans and valuation of the price of a bond, estimate of the term structure of the rates. Control / immunization of interest rate risk: duration and convexity.
Criteria for choosing between financial operations / projects: NPV, IRR, TRM, WACC.
4. Linear Programming (PL) and Operational Research (RO). The formulation of the problem of PL, the mathematical structure, the graphic solution, the properties of the model, the typical applications, the method (the algorithm) of the simplex. Introduction to RO techniques: graphs and their applications, inventory theory, queue theory, Markov processes.
5. Portfolio selection. Investments in activities with a random return. Expected return and volatility / risk of a portfolio of assets. Risk aversion and the Markowitz model. Yield and risk of a portfolio with: a business with a random return and a reliable return, two assets with a random return, two assets with a random return and one with a certain return. Capital Allocation Line. Capital Market Line.

Textbooks
Teaching material is available online by accessing the course web page.
Furthermore, you can consult:
➢ as regards points 2, 3 and 5: Giacomo Scandolo, matematica Finanziaria, Amon, Padova, 2013 and, of the same Author, Matematica Finanziaria: esercizi, Amon, Padova, 2013.
➢ for the theoretical synthesis and exercises about points 2 and 3 we recommend: A. Basso, P. Pianca, Introduzione alla Matematica Finanziaria, Cedam, Padova, 2010.
➢ as regards point 5, we can also see: F. Rossi, F. Mantovani, Teoria di Portafoglio (diversificazione degli investimenti e controllo del profilo rendimento-rischio), Monduzzi Editore, 2010, pages 1-46 and 75-86.
➢ as regards point 4, refer to the online material or the volume of R.E. Markland, Topics in Management Science, J. Wiley & Sons, ed. 1989 or later.

Methods of carrying out the lessons
The course consists of 48 hours of lessons. Tutoring hours are also provided.

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.

#### 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.