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# Dynamic Programming and Applications

2020/2021
RUS
Instruction in Russian
4
ECTS credits
Course type:
Elective course
When:
1 year, 4 module

### Программа дисциплины

#### Аннотация

In this course we will go over the basics of the dynamic programming, a method of solving problems with intertemporal trade-offs, will see how it can be applied to a wide range of real-life situations, and then move to some of the most popular (macro)economic applications of the method. There are no prerequisites to this course, although some very basic knowledge of calculus and basic macro is welcome.

#### Цель освоения дисциплины

• The main aim of "Dynamic Programming and Applications" course is to provide students with the overview of the standard methods for the solution of problems with intertemporal trade-offs.

#### Планируемые результаты обучения

• By the end of the course student will understand the basics of the dynamic programming, will be able to define and solve problems with intertemporal trade-offs.
• To get the students acquainted with the method of dynamic programming for solving problems with intertemporal trade-offs.
• To give the understanding of the applicability of the dynamic programming in various fields of economics, business and IT.
• To introduce the students into the basics of macroeconomic modelling with the relation to the dynamic programming method.
• To define further directions for self-study and professional development in the field of structural macroeconomic modelling with a stress on the applicability of the studied numerical methods.

#### Содержание учебной дисциплины

• Introduction to Dynamic Programming, Part 1.
Introduction to the concept of DP, scope of application; Motivational examples: inventory control, deterministic scheduling problem; More of motivational examples: machine replacement, chess match strategy.
• Introduction to Dynamic Programming, Part 2.
Definition of the basic problem of DP in discrete time; The DP algorithm, principle of optimality; Applying the DP algorithm on the deterministic scheduling example; The DP algorithm with inventory control; Linear quadratic problem.
• DP in (Macro)Economics, Part 1.
Indirect utility: firms and consumers; Cake-eating problem: direct attack vs. DP approach; Cake-eating problem with infinite horizon; Example of analytical solution for the DP problem.
• DP in (Macro)Economics, Part 2.
Taste shocks and discrete choice; General formulation: stationarity and discounting; Consumption problem: two-period problem, stochastic income, infinite horizon, endogenous labor supply.
• Numerical Methods.
Value function iteration: general principle and illustration on cake-eating problem; Policy function iteration: principle and advantages over the value function iteration.
• Introduction to the problem of optimal control.
Definition of the simplest problem in continuous time; Hamiltonian function and the maximum principle; Application to the problem of energy use and environmental quality.
• DP Applications.
Investment problem; Dynamics of employment adjustment; Price setting problem; McCall labor search model; Inflation and unemployment: Phillips tradeoff.

#### Элементы контроля

• In-class Participation
• Midterm
• Final Exam

#### Промежуточная аттестация

• Промежуточная аттестация (4 модуль)
0.5 * Final Exam + 0.15 * Homework Tasks + 0.1 * In-class Participation + 0.25 * Midterm

#### Рекомендуемая основная литература

• Chiang, A. C. (2012). Elements of dynamic optimization. Waveland Press.
• Dynamic economics : quantitative methods and applications, Adda, J., 2003
• Kenneth L. Judd. (1998). Numerical Methods in Economics. The MIT Press.

#### Рекомендуемая дополнительная литература

• Bertsekas, D. P. (2017). Stable Optimal Control and Semicontractive Dynamic Programming.