Ateneo - UPO

First module: financial mathematics.

Second module: linear algebra.

Third module: real functions of multiple real variables and their optimization.

M. D’Amico, G. Fusai e G. Longo, Dispense di Calcolo Finanziario, Algebra Lineare e Ottimizzazione, anno 2015, disponibili nella pagina Moodle del corso.
F. Privileggi, Matematica per l’Economia. Gruppo editoriale Esselibri – Simone, 2008.Il testo è reperibile in biblioteca
S. Margarita - E. Salinelli, MultiMath: Matematica Multimediale per l’Università, Springer, 2004. Available at university library.

1 - a full comprehension of the basic mathematical results regarding the course contents;
2 - being able to choose and use the right tool for solving simple problems related to the course programme;
3 - being able to adapt the instruments to the occurring variants;
4 - being able to adequately and rigorously communicate the logic steps of a problem resolution.

The course Metodi matematici 1 has to be passed.

Lectures and tutorials.

On the course's page on the website www.dir.uniupo.it all the infos related to the course can be found as well as supplementary didactict resources.
Past exams with solutions are available for downloading.

A mandatory written exam and an optional oral exam.

Written part (mandatory):
- 21 exercise (only the best 9 answers are considered) for verifying the knowledge and the comprehension of the course contents as well as the ability to apply these knowledge and autonomously select the best tools to problems solving.

Oral part (optional):
- questions on the course content in order to verify the ability of autonomous analysis and the communication skills.
- analysis of situations which differ from the classical ones in order to verify the ability of learning.

At any time the professor can request, if the situation requires it, an extra evaluation, written or oral.

Fist part - Linear Algebra. Vectors, matrixes and operations. Linear combination, linear independence, rank. Linear systems; Rouché-Capelli theorem; Gaussian solving method. Application to economics and finance.

Second part – Optimization. Real functions of several real variables. Extreme points, with and without constraints. Weierstrass theorem. Differential calculus and extrem points search, substitution method. Linear programming with 2 variables. Applications to business, economics and finance.

Third part – Financial Mathematics. Discount and capitalization operations. Usual financial laws (simple, compound and commercial laws), equivalent rates. Annuities. Amortization of debts, italian and french amortizing schemes. Variable interest rate debts. Financial operations and decisions. Internal interest rate, italian TAEG. Decisions: net present value (NPV) and adjusted present value (APV). Gordon model. Term structure of interest rates, spot and forward rate. Bond pricing. Bond pricing with default risk.

The student at the end of the course should be ablo to make some simple matrix calculation and solve linerar systems. The student should also know how to analyse a real funcion of several variables, being able to identify its extreme points. Finally, the student should know the standard financial laws and parameters and make financial choices among several projects.