Modelli dinamici discreti - ENG

Discrete Dynamical Models

Prof. Ernesto Salinelli

Course Code: EC0004
Subject code: SECS-S/06
6 ECTS – 48 hours
Location: Novara

Educational aims
The course provides the main formal tools for the understanding and the analysis of some discrete-time dynamic models typical of the economic and financial literature, introducing also to the use of a spreadsheet as a support.


Content of the course
RECURSIVE PHENOMENA AND DIFFERENCE EQUATIONS (Chapter 1)  
Examples (simple and compound interest rate, loan, cobweb model, demographic models,   Fibonacci numbers, gambler ruin’s, Hanoi tower), motivations and general definitions.  Graphical method and its implementation with a spreadsheet.
LINEAR DIFFERENCE EQUATIONS (Paragraphs 2.1, 2.2, 2.3, 2.4, 2.6, 2.9)
Homogeneous and non-homogeneous linear difference equations with constant coefficients, one or more steps; linear equations with variable coefficients. Analysis of some economic models (cobweb model, dynamic of the debt/GDP ratio). Using the spreadsheet to build and analyze models.
DISCRETE DYNAMICAL SYSTEMS  (Chapter 3 except paragraph 3.9, paragraph 4.1)
Non linear scalar models: equilibria and periodic orbits, local and global stability analysis, graphical analysis. Applications: logistic model, harvesting strategies.
VECTOR DISCRETE DYNAMICAL SYSTEMS  (Paragraphs 5.1, 5.3, 5.4, 5.5, 5.6 and 5.7)
Some elements of Linear algebra. Vector linear models with constant coefficients: closed form solution, equilibria and their stability. Applications: Cournot duopoly model. Positive models and their application.
MARKOV CHAINS (Chapter 6 and  paragraphs 7.2 and 7.4)
Stochastic matrices, absorbing states, invariant probability distributions. Asymptotic analysis. Graphs. Applications: rating model, brand transition model, Bonus-Malus, Google.


Prerequisites
The course of Mathematics 1 is a prerequisite.

Course Texts
Salinelli E., Tomarelli F., Modelli Dinamici Discreti, Springer, 2013.


Further information can be found in the web page of the course at the URL:

https://eco.dir.unipmn.it/


Teaching methods

Lectures, tutorials and laboratory.

Examination

The exam test consists in:
• an oral examination on two chapters chosen by the student from among those listed
or
• an oral examination on a chapter chosen by the student from among those listed and the preparation and oral discussion of a dissertation on a topic (related to a chapter other than the one chosen) to be agreed with the teacher before the end of the course and to be delivered at least one week before to its discussion.