Training and Research
PhD Programme Courses/classes
Advice to Young Economists
Credits: 4
Language: English
Teacher: Marco Piovesan
Behavioral and Experimental Economics
Credits: 5
Language: Italian
Teacher: Simone Quercia, Maria Vittoria Levati, Marco Piovesan
Development Economics
Credits: 5
Language: English
Teacher: Federico Perali
Finance
Credits: 5
Language: English
Teacher: Cecilia Mancini
Game Theory
Credits: 5
Language: Inglese
Teacher: Francesco De Sinopoli
Inequality
Credits: 5
Language: English
Teacher: Francesco Andreoli, Claudio Zoli
Introduction to Probability – Module II (attività formativa per la Scuola di Dottorato)
Credits: 2
Language: Italian
Teacher: Claudia Di Caterina
Introduction to Probability – Module I
Credits: 2
Language: English
Introduction to Statistical Inference
Credits: 2
Language: English
Teacher: Marco Minozzo
Macroeconomics I
Credits: 7.5
Language: English
Teacher: Tamara Fioroni, Alessia Campolmi
Mathematics
Credits: 7.5
Language: English
Teacher: Letizia Pellegrini, Alberto Peretti
Microeconomics 1
Credits: 10.5
Language: English
Teacher: Simona Fiore, Claudio Zoli, Martina Menon
Political economy
Credits: 5
Language: English
Teacher: Emanuele Bracco, Roberto Ricciuti
Probability
Credits: 7.5
Language: English
Teacher: Marco Minozzo
Mathematics (2022/2023)
Academic staff
Referent
Credits
7.5
Language
English
Class attendance
Free Choice
Location
VERONA
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
Didactic methods
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
