Mathematical methods and modeling

A.A. 2015/2016
Insegnamento per
9
Crediti massimi
80
Ore totali
SSD
SECS-S/06
Lingua
Inglese
Obiettivi formativi
Students will learn advanced mathematical techniques and how to use them to model and solve problems in economics and finance.

Struttura insegnamento e programma

Edizione attiva
Responsabile
Moduli o unità didattiche
Unita' didattica Dynamical Systems
SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE - CFU: 3
Lezioni: 20 ore
Docente: La Torre Davide

Unita' didattica Optimization
SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE - CFU: 6
Esercitazioni: 40 ore
Lezioni: 20 ore
Docente: La Torre Davide

STUDENTI FREQUENTANTI
Propedeuticità
Calculus I.
Prerequisiti e modalità di esame
Closed book exam.
Metodi didattici
Lecture, tutorial, and lab.
Unita' didattica Optimization
Programma
Topics in linear algebra. Review of basic linear algebra. Linear independence. The rank of a matrix. Main results on linear systems. Eigenvalues. Diagonalization. Quadratic forms. Quadratic forms with linear constraints. Partitioned matrices and their inverses.
Linear programming. A simple maximization problem. Graphical solution procedure. Extreme points and the optimal solution. Special cases. General linear programming notation. Sensitivity analysis and interpretation of solution.
Multivariable calculus. Gradients and directional derivatives. Convex sets. Concave and convex functions. Quasiconcave and quasiconvex functions. Taylor's formula. Implicit and inverse function theorems. Degrees of freedom and functional dependence. Differentiability. Existence and uniqueness of solutions of systems of equations.
Static optimization. Extreme points. Local extreme points. Equality constraints: the Lagrange problem. Local second-order conditions. Inequality constraints: nonlinear programming. Sufficient conditions. Comparative statics. Nonnegativity constraints. Concave programming. Precise comparative statics results. Existence of Lagrange multipliers.
Multicriteria decisions. Goal programming: formulation and graphical solution. Goal programming: solving more complex problems. Scoring models. Analytic hierarchy process AHP. Establishing priorities using AHP. Using AHP to develop an overall priority ranking.
Numerical examples and application to marketing, finance, and operations management with LINGO.
Metodi didattici
Lecture, tutorial, and lab.
Materiale didattico e bibliografia
Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Further Mathematics for Economic Analysis, Financial Times Prentice Hall, 2008 (chapters 1,2,3).
Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, Kipp Martin, An Introduction to Management Science: Quantitative Approaches to Decision Making, Cengage Learning, 2010 (chapters 2,3,4,5,8,14).
Unita' didattica Dynamical Systems
Programma
Differential equations I: First-order equations in one variable. Introduction. The direction is given, find the path. Separable equations. First-order linear equations. Exact equations and integrating factors. Transformation of variables. Qualitative theory and stability. Existence and uniqueness.
Differential equations II: Second-order equations and systems in the plane. Introduction. Linear differential equations. Constant coefficients. Stability for linear equations. Simultaneous equations in the plane. Equilibrium points for linear systems. Phase plane analysis. Stability for nonlinear systems. Saddle points.
Control theory: basic techniques. The basic problem. A simple case. Regularity conditions. The standard problem. The maximum principle. Sufficient conditions. Variable final time. Current value formulations. Scrap values. Infinite horizon. Phase diagram.
Metodi didattici
Lecture, tutorial, and lab.
Materiale didattico e bibliografia
Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Further Mathematics for Economic Analysis, Financial Times Prentice Hall, 2008 (chapters 5,6,9).
STUDENTI NON FREQUENTANTI
Prerequisiti e modalità di esame
Closed book exam.
Unita' didattica Optimization
Programma
Topics in linear algebra. Review of basic linear algebra. Linear independence. The rank of a matrix. Main results on linear systems. Eigenvalues. Diagonalization. Quadratic forms. Quadratic forms with linear constraints. Partitioned matrices and their inverses.
Linear programming. A simple maximization problem. Graphical solution procedure. Extreme points and the optimal solution. Special cases. General linear programming notation. Sensitivity analysis and interpretation of solution.
Multivariable calculus. Gradients and directional derivatives. Convex sets. Concave and convex functions. Quasiconcave and quasiconvex functions. Taylor's formula. Implicit and inverse function theorems. Degrees of freedom and functional dependence. Differentiability. Existence and uniqueness of solutions of systems of equations.
Static optimization. Extreme points. Local extreme points. Equality constraints: the Lagrange problem. Local second-order conditions. Inequality constraints: nonlinear programming. Sufficient conditions. Comparative statics. Nonnegativity constraints. Concave programming. Precise comparative statics results. Existence of Lagrange multipliers.
Multicriteria decisions. Goal programming: formulation and graphical solution. Goal programming: solving more complex problems. Scoring models. Analytic hierarchy process AHP. Establishing priorities using AHP. Using AHP to develop an overall priority ranking.
Numerical examples and application to marketing, finance, and operations management with LINGO.
Materiale didattico e bibliografia
Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Further Mathematics for Economic Analysis, Financial Times Prentice Hall, 2008 (chapters 1,2,3).
Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, Kipp Martin, An Introduction to Management Science: Quantitative Approaches to Decision Making, Cengage Learning, 2010 (chapters 2,3,4,5,8,14).
Unita' didattica Dynamical Systems
Programma
Differential equations I: First-order equations in one variable. Introduction. The direction is given, find the path. Separable equations. First-order linear equations. Exact equations and integrating factors. Transformation of variables. Qualitative theory and stability. Existence and uniqueness.
Differential equations II: Second-order equations and systems in the plane. Introduction. Linear differential equations. Constant coefficients. Stability for linear equations. Simultaneous equations in the plane. Equilibrium points for linear systems. Phase plane analysis. Stability for nonlinear systems. Saddle points.
Control theory: basic techniques. The basic problem. A simple case. Regularity conditions. The standard problem. The maximum principle. Sufficient conditions. Variable final time. Current value formulations. Scrap values. Infinite horizon. Phase diagram.
Materiale didattico e bibliografia
Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Further Mathematics for Economic Analysis, Financial Times Prentice Hall, 2008 (chapters 5,6,9).
Periodo
Primo trimestre
Periodo
Primo trimestre
Modalità di valutazione
Esame
Giudizio di valutazione
voto verbalizzato in trentesimi
Docente/i
Ricevimento:
In aspettativa. Il ricevimento e' sospeso.
Stanza 30, DEMM