Università di Pavia - Offerta formativa

DECISIONS AND CHOICES

Anno immatricolazione

2021/2022

Anno offerta

2022/2023

Normativa

DM270

SSD

SECS-S/06 (METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE)

Dipartimento

DIPARTIMENTO DI MATEMATICA 'FELICE CASORATI'

Corso di studio

MATEMATICA

Curriculum

PERCORSO COMUNE

Anno di corso

2°

Periodo didattico

Secondo Semestre (01/03/2023 - 09/06/2023)

Crediti

6

Ore

44 ore di attività frontale

Lingua insegnamento

INGLESE

Tipo esame

SCRITTO

Docente

Prerequisiti

The contents of the Mathematics basic course and some elementary models in Microeconomics together with some basic knowledge in elementary probability theory are considered as preliminaries.

Obiettivi formativi

The course will offer an organic overview of some tools used in economics and finance models to develop a rational choice theory. The methodological part devoted to the introduction of some fundamental mathematical tools will be completed by examples and applications in economics and finance. The aim of the course is to learn how some important mathematical tools are used in economics and finance. The focus will be on modelling simple situations by use of simple mathematical tools. Besides some optimization and linear algebra techniques, some general skills such as the formalization of a model and use of deductive reasoning will be acquired by the students.

Programma e contenuti

LINEAR MODELS WITH APPLICATIONS TO ECONOMICS AND FINANCE

Matrices and partitioned matrices: basic calculus rules. Linear functions and linear systems: a review. Quadratic forms. Eigenvalues and eigenvectors. Diagonalization of a quadratic form. Applications to models in economics and finance.

OPTIMIZATION MODELS WITH APPLICATIONS TO ECONOMICS AND FINANCE

Functions of many variables: calculus rules. Optimization models without constraints. Implicit functions and comparative statics. Constrained optimization and Lagrange multipliers. Applications to models in economics and finance.

DECISIONS UNDER RISK

Utility and preference representation; Decisions under risk; Von Neumann-Morgenstern model, Absolute and relative risk aversion. Hints on modern approaches to decision theory.

Matrices and partitioned matrices: basic calculus rules. Linear functions and linear systems: a review. Quadratic forms. Eigenvalues and eigenvectors. Diagonalization of a quadratic form. Applications to models in economics and finance.

OPTIMIZATION MODELS WITH APPLICATIONS TO ECONOMICS AND FINANCE

Functions of many variables: calculus rules. Optimization models without constraints. Implicit functions and comparative statics. Constrained optimization and Lagrange multipliers. Applications to models in economics and finance.

DECISIONS UNDER RISK

Utility and preference representation; Decisions under risk; Von Neumann-Morgenstern model, Absolute and relative risk aversion. Hints on modern approaches to decision theory.

Metodi didattici

The course will consist in lectures and problem sessions.

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 economic modelling.

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 economic modelling.

Testi di riferimento

P. Simon and L. Blume, Mathematics for economists , New York ; London : Norton, 1994.

D. Kreps, Notes on the theory of choice, Westview Press 1988

D. Kreps, Notes on the theory of choice, Westview Press 1988

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.

Altre informazioni

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Obiettivi Agenda 2030 per lo sviluppo sostenibile