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, available on the DIR repository.
Addtional useful references
F. Privileggi, Matematica per l’Economia. Gruppo editoriale Esselibri – Simone, 2008.

S. Margarita - E. Salinelli, MultiMath: Matematica Multimediale per l’Università, Springer, 2004.

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 exam Metodi Matematici 1 has to be passed before taking Metodi Matematici 2.

Face to face lectures with integrated exercises.

All the infos related to the course as well as supplementary resources
can be found on the course's page on the website www.dir.uniupo.it.

Solved exercised and past exams with solutions are also available for downloading.

See the web page of the course at www.dir.uniupo.it

First part – Financial Mathematics. Discount and capitalization operations. Usual financial laws (simple and compounded 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.
Second part - Linear Algebra. Vectors, matrices and operations. Linear combination, linear independence, rank. Linear systems; Rouché-Capelli theorem; Gaussian solving method. Application to economics and finance.

Third 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.

KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
1. Recognize the proper meaning of standard indices of cost/profitability for a financial operation such as NPV, IRR, etc..
2. Identify the proper meaning of terms such as yields, default risk and so on.
Reproduce the correct procedures for solving linear systems and financial and optimization problems.

APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to apply the learned methods to compute quantities relevant both in theory and in practice such as: the price of a bullet bond, the internal effective rate of a loan, the probability of default, the extra-performance of a fund, assess the profitability of a project.