Financial mathematics (2008/2009)

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Course not running

Course code
4S00393
Credits
10
Coordinator
Francesco Rossi
Course news Seminars related to the course
Teaching is organised as follows:
Unit Credits Academic sector Period Academic staff
1 - lezione 4 SECS-S/06-MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES Primo semestre Francesco Rossi
2 - esercitazione 1 SECS-S/06-MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES Primo semestre Alberto Roveda
3 - lezione 4 SECS-S/06-MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES Primo semestre Alberto Peretti
4 - esercitazione 1 SECS-S/06-MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES Primo semestre Alberto Peretti

Learning outcomes

Module: 2 - esercitazione
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Module: 3 - lezione
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This module of the course provides the mathematical tools to analyze the economic and financial models presented in the subsequent two year of Laurea magistrale. It is focused on some advanced topics in linear algebra and it provides a fairly wide overview on the main theoretical results and operative techniques in both unconstrained and constrained optimization. Students are encouraged to attend this course after having obtained a positive grade in Mathematics.


Module: 4 - esercitazione
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Module: 1 - lezione
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Syllabus

Module: 2 - esercitazione
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Module: 3 - lezione
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1. Functions of more than one variable
Metric and topology in R^n. Functions of more than one variable: domain, graphic, level sets, limits and continuity. Partial derivatives. Differentiability, continuity and tangent subspace. Calculus of derivatives. Directional derivatives and gradient. Vector valued functions. Jacobian matrix.

2. Linear algebra
Linearly dependent and independent vectors. Basis and dimension of a linear space. Orthogoonal vectors, orthogonal projections, orthonormal basis. Linear transformations and matrices. Kernel and rank of a linear transformation. Change of basis. Similar matrices. Decomposizione di un’applicazione lineare: autovettori e autovalori. Diagonalizzazione di una matrice.


Module: 4 - esercitazione
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Module: 1 - lezione
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Assessment methods and criteria

Module: 2 - esercitazione
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Module: 3 - lezione
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The final examination consists of a written test and an oral test. The access to the oral test is conditional of a positive outcome on the written test.


Module: 4 - esercitazione
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Module: 1 - lezione
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