Master
2021/2022
Mathematics for Economists
Type:
Compulsory course (Financial Economics)
Area of studies:
Economics
Delivered by:
International College of Economics and Finance
When:
1 year, 1, 2 module
Mode of studies:
offline
Open to:
students of one campus
Master’s programme:
Financial Economics
Language:
English
ECTS credits:
7
Contact hours:
112
Course Syllabus
Abstract
The objective of the course is to equip the students with the essential mathematical background for Economics, Econometrics and Finance: preliminaries on linear algebra, multivariate calculus, probability theory and statistics, dynamic optimization, and stochastic calculus. Prerequisites include undergraduate level mathematics: Calculus (both single and multi-dimensional), Linear Algebra, Probability theory and Mathematical Statistics, Ordinary Differential Equations.
Learning Objectives
- Get acquainted with the essential mathematical tools for Economics, Econometrics and Finance
- Develop skills at solving differential equations and systems of differential equations
- Understand the dynamics induced by systems of differential equations
- Become familiar with basic methods on optimal control theory and dynamic programming and their applicability in economic theory
- Become familiar with Brownian and Wiener stochastic processes and Ito’s integral, both at a preliminary theoretical level, and in terms of simple applications
Expected Learning Outcomes
- Apply multidimensional calculus, optimization to economic problems
- Apply statistical methods to economic tasks
- Solve problems of calculus of variations as well as optimal control theory
- Become familiar with the main elementary notions related to matrices and linear algebra that are employed in Economics and Econometrics
- Become familiar with the main elementary ideas and techniques for constrained optimization that are employed in Economics
- Solve elementary ordinary differential equations and understand the dynamics induced by a system of equations
- Understand the balancing of intertemporal trade-offs via the Euler equation and the recursive formulation of the problems via Bellman's equation
- Solve problems of calculus of variations and optimal control theory, and interpret the multiplier function as a reflection of incentives
Course Contents
- Multidimensional calculus, basics of optimization
- Convex analysis and Kuhn-Tucker theorem
- Linear Algebra
- Theory of probability and statistics
- Differential Equations
- Dynamic Optimization in Continuous Time
- Dynamic Optimization in Discrete Time
- Uncertainty, information, and stochastic calculus
Interim Assessment
- 2021/2022 1st module0.25 * home assignments + 0.33 * refersher test + 0.42 * Midterm Examination
- 2021/2022 2nd module0.15 * home assignments + 0.4 * Final exam + 0.25 * Midterm Examination + 0.2 * refersher test
Bibliography
Recommended Core Bibliography
- Dynamic optimization : the calculus of variations and optimal control in economics and management, Kamien, M. I., 2012
- Economic growth, Barro, R. J., 2004
- Introduction to modern economic growth, Acemoglu, D., 2009
- Mathematics for economists, Simon, C. P., 1994
- Statistics for business and economics, Newbold, P., 2003
Recommended Additional Bibliography
- Stochastic calculus for finance. Vol.1: The binomial asset pricing model, Shreve, S. E., 2004