ISCTE-IUL > Education > DEc , DF

Mathematics and Numerical Methods for Economics and Finance II (2 º Sem 2017/2018)

Code:	03092
Acronym:	03092
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.

Semester	ECTS Credits	Theoretical Lesson (T)	Theoretical and Pratical Lesson (TP)	Practical and laboratorial lesson (PL)	Seminary (S)	Field Work (TC)	Training Period (E)	Tutorial Orientation (OT)	Contact Hours	Autonomous Work	Others (O)	Total Load Hours [?]Contact Hours + Autonomous Work
1	6.0	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	125.0 h/sem	0.0 h/sem	150.0 h/sem


Since year	2017/2018
Pre-requisites	Basic knowledge of calculus, linear algebra, probability and programming are welcome.
Objectives	This course teaches optimization in Rn, diference equations, ordinary differential equations and dynamic programming, in the context of economics and financial applications. It will emphasize both the most fundamental analytic aspects of the underlying subjects as well as the development of numerical methods in MATLAB. It is directed at first year Phd students in economics and finance.
Program	I. Optimization in R^n. (a) Unconstrained optimization: - Necessary and sufficient conditions. - Steepest descent, Newton and quasi-Newton methods. (b) Non-linear constrained optimization: - The Karush-Kuhn-Tucker conditions. - Penalty methods. II.Difference equations. (a) Linear difference equations. (b) Some notable non-linear equations. (c) Equilibrium points. (d) Markov Chains. (e) Applications: compound interests and gambler's ruin. III Ordinary differential equations. (a) Some notable ODEs (b) Existence, uniqueness and qualitative methods. (c) Euler's method and friends. (d) Applications: dynamical interest rates, geometric Brownian motion, demographic models and turbulence. IV. Dynamical programming. (a) Dynamical programming in discrete time. (b) Dynamical programming in continuous time. (c) Optimal control (d) Numerical methods. (e) Applications: modelling sustainable development and money in the utility.
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. 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. Nocedal, J. and Wright, S. "Numerical optimization", Springer (1999) 2. Banasiak, J. "Mathematical modelling in one dimension: an introduction via difference and differential equations", Cambridge University Press (2013). 3. Miao, J. "Economic dynamics in discrete time", MIT press (2013)
Complementar Bibliographic	4. Heer, R. and Maussner, A. "Dynamic General Equilibrium Modeling Computational Methods and Applications", Springer (2005). 5. Acemoglu, D. "Introduction to Modern Economic Growth", Princeton University Press (2009). 6. Burden, R.L.; Faires, J.D. "Numerical Analysis", Prindle, Weber & Schmidt, Boston (1993).