MATHEMATICAL METHODS FOR FINANCE

Description

Objectives: 1) To learn some basic methods in Linear Algebra, Linear and Nonlinear Dynamical Systems, Optimization. These are essential tools to understand and develop mathematical models in economics. 2)To be able to understand mathematical models and to develop them in simple cases Assessment: 33% project assigned during the course: 67% final exam: written and oral Teaching Methods: Lessons and Exercises sessions. “Teaching is not transferring knowledge, but creating the conditions for its production or construction” Prerequisites: All basic mathematics courses of Laurea Triennale in Economics and similar topics. In particular: - Calculus for one variable functions (basic topology, functions and their properties, limits derivatives and their connection with monotonicity and convexity, integrals, graph of functions); - Searching extremals and zeros for one-variable functions using the appropriate theorems; - Basic linear algebra concepts (vector spaces and their bases, linear dependence and independence of vectors, matrices, rank, determinant, linear systems, Rouché-Capelli Theorem) - Basic calculus for several variables: topology in R^n, limits, continuity, differentiability, gradient and its properties (this part will be briefly reviewed in the first lectures) Contents: - Review of calculus of Several Variables - Implicit Functions and Comparative Statics - Unconstrained Optimizazion - Constrained Optimization - Eigenvalues and eigenvectors, - Spectral decomposition - Linear/Nonlinear Difference/Differential Equations and Systems - Use of the above techniques to build mathematical models of real phenomena. Reference Texts: 1) MATEMATICS FOR ECONOMISTS Carl Simon e Lawrence Blume W.W. NORTON & COMPANY. 2) Notes given by the teacher. Thesis assignment criteria: Interview Extended Program And Reference Reading Material: Week 1: - Calculus of Several Variables 1 Extended Program And Reference Reading Material: Week 10: - Linear Difference/Differential Equations and Systems 2 Extended Program And Reference Reading Material: Week 11: - Nonlinear Difference/Differential Equations and Systems 1 Extended Program And Reference Reading Material: Week 12: - Nonlinear Difference/Differential Equations and Systems 2 Extended Program And Reference Reading Material: Week 2: - Calculus of Several Variables 2 Extended Program And Reference Reading Material: Week 3: - Implicit Functions and Comparative Statics Extended Program And Reference Reading Material: Week 4: - Unconstrained Optimizazion Extended Program And Reference Reading Material: Week 5: - Constrained Optimization 1 Extended Program And Reference Reading Material: Week 6: - Constrained Optimization 2 Extended Program And Reference Reading Material: Week 7: - Eigenvalues and eigenvectors 1 Extended Program And Reference Reading Material: Week 8: Eigenvalues and eigenvectors 2 Extended Program And Reference Reading Material: Week 9: - Linear Difference/Differential Equations and Systems 1 Intended learning outcomes: 1) Knowledge and understanding: The course will offer the basic theoretical tools of Linear Algebra, Dynamical Systems, Optimization. These are key tools to understand and develop mathematical models in economics. 2) Applying knowledge and understanding: The students will be taught how to use the above basic tools to develop simple mathematical models of real phenomena such as: - population and investment dynamics; - climate change; - ranking of web pages; - economic dynamics; 3) Making judgements: We expect students to be able to - understand the main mathematical features of basic economic models; - judge the reliability of information on quantitative modeling that they read in the press; - build simple mathematical models of real phenomena. 4) Communications Skills: This course will give the students the possibility to acquire and understand major terms and concepts in order to communicate their ideas, proposals, analysis and critical reasoning in the field of mathematical modeling in the most effective and appropriate way. 5) Learning skills: This course will contribute to empower learners giving them the tools to evaluate the statements on quantitative mathematical modeling (that they can read in the press or in specialized journals) in an independent way.