Mathematical Methods and Modeling

A.Y. 2015/2016
Lesson for
9
Max ECTS
80
Overall hours
SSD
SECS-S/06
Language
English
Learning objectives
Students will learn advanced mathematical techniques and how to use them to model and solve problems in economics and finance.

Course structure and Syllabus

Active edition
Yes
Responsible
Unita' didattica Dynamical Systems
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES - University credits: 3
Lessons: 20 hours
Professor: La Torre Davide
Unita' didattica Optimization
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES - University credits: 6
Practicals: 40 hours
Lessons: 20 hours
Professor: La Torre Davide
ATTENDING STUDENTS
Unita' didattica Optimization
Syllabus
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.
Unita' didattica Dynamical Systems
Syllabus
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.
NON-ATTENDING STUDENTS
Unita' didattica Optimization
Syllabus
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.
Unita' didattica Dynamical Systems
Syllabus
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.
Lesson period
First trimester
Lesson period
First trimester
Assessment methods
Esame
Assessment result
voto verbalizzato in trentesimi
Professor(s)
Reception:
On leave. Office hours are suspended.
Room 30, DEMM