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Mathematics and Numerical Methods for Economics and Finance I
(1
º Sem
2018/2019)
Code:
03091
Acronym:
03091
Level:
3rd Cycle
Basic:
No
Teaching Language(s):
English
Friendly languages:
Be English-friendly or any other language-friendly means that UC is taught in a language but can either of the
following conditions:
1. There are support materials in English / other language;
2. There are exercises, tests and exams in English / other language;
3. There is a possibility to present written or oral work in English / other language.
1
9.0
0.0 h/sem
24.0 h/sem
0.0 h/sem
0.0 h/sem
0.0 h/sem
0.0 h/sem
1.0 h/sem
25.0 h/sem
200.0 h/sem
0.0 h/sem
225.0 h/sem
Since year
2018/2019
Pre-requisites
Basic knowledge of calculus, linear algebra, probability and programming are welcome.
Objectives
This course starts by reviewing some basic results in one dimensional analysis and in linear algebra. It then teaches vector calculus and measure and integration. It also puts some emphasis in numerical methods, in particular those used in Monte Carlo simulations. It is directed at first year PhD students in economics and finance.
Program
I. Introduction to MATLAB. II. One dimensional problems. (a) Review of single variable calculus (b) Numerical solutions of equations in one variable: III. Systems of linear and non-linear equations (a) Some basic notions of linear algebra (b) Direct and iterative methods for solving linear systems. (c) Review of vectorial calculus. (d) Newton's method for systems of (non-linear) equations. IV. Metric spaces (a) Basic notions (b) Convergence in function spaces. V. Measure, Probability and Integration (a) Riemann's integral. (b) Introduction to Measure Theory and the Lebesgue integral. (c) Probability theory: (d) Generation of random variables. (e) Monte Carlo Methods.
Evaluation Method
The final grade will be based on individual homework assignments (75%) and a final exam (25%) with a minimal grade of 8/20. The evaluation of the homework assignments might be subjected to oral discussions. Due the nature of the evaluation in this course, there is no 2nd chance exam.
Teaching Method
The classes are run as theoretical-practical lectures. The theoretical exposition is followed by computer lab sessions, using MATLAB.
Observations
-
Basic Bibliographic
1) Richard Burden, J. Douglas Faires, Annette Burden (2015). Numerical Analysis, Cengage Learning. 2) J. E. Marsden and A. Tromba, Vector Calculus, 5a ed., W. H. Freeman and Company (2003). 3) M. Adams and V. Guillemin (1996).Measure Theory and Probability, Wadsworth & Brooks, 4) Ross, S. M (1997). Simulation. San Diego: Academic Press.
Complementar Bibliographic
5) Paolo Brandimarte (2006). Numerical Methods in Finance and Economics: A MATLAB-Based Introduction, John Wiley & Sons. 6) Kolmogorov, A. N. (1970). Introductory real analysis. Englewood Cliffs, N.J. :Prentice-Hall. 7) Mario J. Miranda and Paul L. Fackler (2002). Applied Computational Economics and Finance, MIT Press.
