SECS-P/01 (ECONOMIA POLITICA)
DIPARTIMENTO DI SCIENZE ECONOMICHE E AZIENDALI
Corso di studio
ECONOMICS, FINANCE AND INTERNATIONAL INTEGRATION - ECONOMIA, FINANZA E INTEGRAZIONE INTERNAZIONALE
Secondo Semestre (22/02/2021 - 22/05/2021)
44 ore di attività frontale
The contents of Matematica Generale course (basic calculus and linear algebra) and some elementary models in Microeconomics together with some basic knowledge in elementary probability theory and statistics are considered as preliminaries.
The course will offer an organic overview of some tools used in finance models to develop a rational choice theory and the study of financial markets. The methodological part devoted to the introduction of some fundamental mathematical tools will be completed by examples and applications. The aim of the course is to learn how some important mathematical tools are used in finance. The focus will be on modelling simple situations by use of simple mathematical tools. Besides some optimization and linear algebra techniques and some notions on dynamical systems and dynamic optimization, some general skills such as the formalization of a model and the use of deductive reasoning will be acquired by the students.
Programma e contenuti
LINEAR AND OPTIMIZATION MODELS
Matrices and partitioned matrices: basic calculus rules. Linear functions and linear systems: a review. Quadratic forms. Eigenvalues and eigenvectors. Diagonalization of a quadratic form.
Functions of many variables: calculus rules. Optimization models without constraints. Implicit functions and comparative statics. Equality constrained optimization and Lagrange multipliers. Inequality constrained optimization and Kuhn-Tucker conditions.
Dynamical systems in the discrete and in the continuous case. Stability analysis.
DYNAMIC OPTIMIZATION: Optimal control problems. The maximum principle. Recursive methods and Bellman's equation.
MODELS and APPLICATIONS
The course will consist in lectures and problem sessions. Due to the coronavirus emergency situation, some activities may be held online and it will be possible to follow the course at distance. The mathematical results, even if formally enunciated, will not be proved since the focus of the course is on the application of quantitative tools to financial modelling.
Testi di riferimento
P. Simon and L. Blume, Mathematics for economists , New York ; London : Norton, 1994.
A. Chiang, Elements of dynamic optimization, Waveland press, 2000.
N. L. Stokey, R. E. Lucas, Recursive Methods in Economic Dynamics, HUP, 1989.
Modalità verifica apprendimento
The exam consists of a written test. Whenever it is possible, the ability to use the quantitative tools introduced in the course to represent and solve a simple economic model will be tested.
Students who attend the lectures can opt for continuous assessment through a mid term test and applied projects.
Obiettivi Agenda 2030 per lo sviluppo sostenibile