Master
2021/2022
Mathematical Economics and Statistics
Type:
Compulsory course (Applied Economics and Mathematical Methods)
Area of studies:
Economics
Delivered by:
Department of Mathematics
When:
1 year, 1, 2 module
Mode of studies:
offline
Open to:
students of one campus
Instructors:
Yaroslavna Pankratova
Master’s programme:
Applied Economics and Mathematical Methods
Language:
English
ECTS credits:
6
Contact hours:
52
Course Syllabus
Abstract
Курс «Математическая экономика и статистика» предназначен для магистрантов, желающих получить базовые знания в области прикладной математики, используемой в экономике. Курс состоит из теории вероятностей, статистики, оптимизации и динамических систем. Включает в себя такие разделы, как: 1. Основы теории вероятностей. 2. Статистика: оценка, доверительные интервалы, проверка гипотез, случайные процессы, временные ряды. 3. Математическое программирование: постановка задачи, классификация задач математического программирования, линейное программирование, выпуклый анализ, теорема Куна-Таккера. 4. Динамические системы: разностные уравнения, системы разностных уравнений, стохастические линейные разностные уравнения, основные методы решения дифференциальных уравнений, динамическая оптимизация.
Learning Objectives
- Being able to perform probabilistic and statistical calculations in standard formulations, give a meaningful interpretation of the results of calculations, process empirical and experimental data.
- Being able to investigate the local behavior and stability of nonlinear dynamical systems in the vicinity of a hyperbolic stationary point.
- Have the skills of probabilistic statistical thinking, have an idea about basic concepts of nonlinear dynamics
Expected Learning Outcomes
- able to define MA, ARMA, ARIMA processes
- can compute conditional and total probabilities, knows basic laws of probabilities
- can compute large sample and small sample confidence interval
- can solve first order linear difference equations and LDE of order p
- can solve nonlinear programming using Lagrange theorem and Kuhn-Tucker conditions
- can solve problems of dynamic programming using Bellman equation
- can solve system of linear difference equations
- can test hypothesis on defined significance level
- can use method of moments and method of of maximum likelihood
- can use simplex algorithm to solve linear programming problem
- know key concepts of mathematical programming
- knows properties of Markov chains, can solve problems
Course Contents
- Probability
- Estimation
- Confidence intervals
- Hypothesis testing
- Time series models
- Markov chains
- Introduction to mathematical programming
- Linear programming
- Nonlinear programming
- Linear difference equations
- System of linear difference equations
- Dynamic programming
Interim Assessment
- 2021/2022 2nd module0.4 * Exam + 0.12 * Activity + 0.12 * Homework 1 + 0.12 * Test 2 + 0.12 * Homework 2 + 0.12 * Test 1
Bibliography
Recommended Core Bibliography
- Ljungqvist, L., & Sargent, T. J. (2012). Recursive Macroeconomic Theory (Vol. 3rd ed). Cambridge, Mass: The MIT Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=550665
Recommended Additional Bibliography
- Takayama,Akira. (1985). Mathematical Economics. Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.cup.cbooks.9780521314985