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Regular version of the site

Mathematical Economics and Statistics

Academic Year
Instruction in English
ECTS credits
Course type:
Compulsory course
1 year, 1, 2 module


Course Syllabus


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

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

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

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
Assessment Elements

Assessment Elements

  • non-blocking Activity
  • non-blocking Exam
  • non-blocking Homework 1
  • non-blocking Homework 2
  • non-blocking Test 1
  • non-blocking Test 2
Interim Assessment

Interim Assessment

  • 2021/2022 1st module
  • 2021/2022 2nd module
    0.12 * Activity + 0.4 * Exam + 0.12 * Homework 1 + 0.12 * Homework 2 + 0.12 * Test 1 + 0.12 * Test 2


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