Academic staff

Letizia Pellegrini, Alberto Peretti

Referent

Letizia Pellegrini

Credits

7.5

Language

English

Class attendance

Free Choice

Location

VERONA

Moodle Seminars 0

Learning objectives

The course aims to provide students with the necessary tools to deal, from a quantitative point of view, with the main problems that arise in the economic and financial framework. After an introduction on some advanced notions of Linear Algebra and Calculus for functions of several variables, unconstrained and constrained optimization problems are introduced and their applicability in the economic-financial field is presented. The solution of optimization problems will be treated with the classical results deriving from the first and second order optimality conditions and from the properties of the Lagrangian function.

Prerequisites and basic notions

The basic notions of Linear Algebra and Calculus for functions of one variable are essential prerequisites.

Program

1. Linear algebra: eigenvalues and eigenvectors of a matrix, quadratic forms, sign of a quadratic form, definite and semidefinite matrices.
2. Differential calculus: functions of several variables, level sets, partial derivatives for functions of several variables, convex functions.
3. Unconstrained optimization: first order optimality conditions, second order optimality conditions.
4. Constrained optimization: the Weierstrass theorem. Optimality problems with equality constraints, Lagrange's theorem. Lagrangian function and optimality conditions. Optimal problems with inequality constraints, the Kuhn-Tucker theorem. Convex problems.

Bibliography

When and where

The course includes 30 hours of classroom lessons, during which both theoretical aspects and appropriate examples and exercises will be presented.

Learning assessment procedures

The exam is written. An intermediate test will be offered during the course; at the end of the course a final test will be scheduled. The final grade is the mean of the two partial grades.

Assessment

The final grade is the mean of the partial grades obtained in the intermediate and final tests.

Criteria for the composition of the final grade

The final grade is first expressed out of thirty and subsequently converted according to the following table:

A + = 30 and honors
A = 29-30
A - = 28
B + = 26-27
B = 25
B - = 23-24
C + = 22
C = 21
C - = 20
D = 18-19
F = failed