The objective of this course is to teach students how to use mathematical tools to model financial markets and solve problems in finance. Finance as a sub-field of economics is concerned with the valuation of assets and financial instruments, as well as the allocation of resources. Fundamental theories about the way economies function and the way we value assets will constitute an essential feature of the course.

- Duration and Immunization techniques.
- Investment decisions under uncertainty: the nature of risk; the maximum return criterion; the modern theory of utility.
- The Mean Variance Criterion; the utility foundations of the MVC.
- Optimization theory, both for unconstrained smooth functions and for problems with equality constraints.
- The M-VC and Portfolio Selection. Markowitz’s teory. The Investment in liquid assets. Portfolio of Two Risky Securities. Portfolio of n Risky Securities. The gain from diversification. The introduction of one riskless asset. The single-Stock portfolio with Lending and Borrowing. The Market Portfolio composition and the Market Line equation.

Analysis
Mathematical Finance 1

It is expected the learning of financial techniques applied both to classical problems and to the modern ones relates with portfolio selection, and the ability of a proper and autonomous use of such theory and mathematical techniques in the working places of this sector of activities.

Modalità didattiche

The course will consist of lectures and home assignment.

Testi di studio

Any textbook covering the topics of the course, for example:
H. Levy and M. Sarnat, Portfolio and Investment Selection: Theory and Practice, Prentice Hall intl.
F.M. Wilkes, Mathematics for Business, Finance and Economics, Intl Thom son Business Press; 2nd edition.

Modalità di
accertamento

Oral exam and written test (either in English or in Italian).

Disabilità e DSA

Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.

A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.