2020/2021
Research Seminar "Stochastic Analysis and its Applications in Economics 2"
Category 'Best Course for New Knowledge and Skills'
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Language:
English
ECTS credits:
3
Contact hours:
36
Course Syllabus
Abstract
This seminar will cover a wide range of problems related to stochastics. The aim of this seminar is to present new developments in this field and to give students an opportunity to learn some modern concepts of stochastic analysis. Special attention will be paid to applications of stochastic models in economics and finance.The talks will be given by the members of the laboratory of stochastic analysis and its applications (lsa.hse.ru), the guests of the laboratory, the stuff of the faculty of mathematics, as well as by students and postdocs. Рrerequisites: Some knowledge in the mathematical analysis, probability theory, stochastic processesis expected.
Learning Objectives
- We aim to attract students and post-graduate students to this seminar, and hope that the seminar will motivate them to provide their own research in stochastics. This seminar serves as the good venue for studying of various topics in stochastic analysis, which are not covered by classical courses. Most talks will be based on recent papers, and therefore this seminar gives a possibility to get an impression of modern developments in this field.
Expected Learning Outcomes
- Students learn about linear programming problems in economics: transportation problem, monopoilist problem etc.
- Students learn about mechanism design
- Students learn about applications of the game theory
- Students learn about applications of heavy tailed distributions in finance
- Students learn about stochstic elasticity
- Students learn about optimal transportation theory
Course Contents
- Linear programming in economics
- Mechanism design
- Heavy tailed distributions with applications in finance
- Optimal transportation
- Stochastic elasticity
- Applications of game theory
Assessment Elements
- Students should make a presentation on the seminar, and will get a mark for it.
- Discussion of a research article
Interim Assessment
- Interim assessment (4 module)0.3 * Discussion of a research article + 0.7 * Students should make a presentation on the seminar, and will get a mark for it.
Bibliography
Recommended Core Bibliography
- A treatise on the mathematical theory of elasticity, Love, A. E. H., 2013
- Game Theory: A Multi-Leveled Approach. (2008). Springer Verlag. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsnar&AN=edsnar.oai.cris.maastrichtuniversity.nl.publications.f0459d98.4840.4780.9538.9cb97d614697
- Handbook of heavy tailed distributions in finance, , 2003
- Mechanism design : a linear programming approach, Vohra, R. V., 2011
- Optimal transport : old and new, Villani, C., 2009
- Двадцать лекций о гауссовских процессах, Питербарг, В. И., 2015
- Исследование операций (линейное программирование и стохастические модели) : учебник / В.А. Каштанов, О.Б. Зайцева. — Москва : КУРС, 2017. - 256 с. - ISBN 978-5-906818-78-2. - Режим доступа: http://znanium.com/catalog/product/1017099
Recommended Additional Bibliography
- An introduction to game theory, Osborne, M.J., 2009
- Исследование операций : (линейное программирование и стохастические модели): учебник для вузов, Каштанов, В. А., 2016