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Regular version of the site
Bachelor 2024/2025

Stochastic processes and applications

Type: Compulsory course (Data Science and Business Analytics)
Area of studies: Applied Mathematics and Information Science
When: 3 year, 1, 2 module
Mode of studies: offline
Open to: students of one campus
Language: English
ECTS credits: 4

Course Syllabus

Abstract

This course is conducted at Data Science and Business Analytics program and is provided to 3rd-year undergraduates who have studied a course covering basic probability and statistical inference. A half of this course introduces concepts of Markov chains, random walks, martingales. The course requires basic knowledge in probability theory and linear algebra. It introduces students to the modeling, quantification and analysis of uncertainty. The main objective of this course is to developthe skills needed to do empirical research in fields operating with a concept of Stochastic processes and its applications. The course aims to provide students with techniques and receipts for estimation and assessment of quality of economic models with time series data.
Learning Objectives

Learning Objectives

  • The main objective of this course is to develop the skills needed to do empirical research in fields of stochastic processes and application in finance
Expected Learning Outcomes

Expected Learning Outcomes

  • Students get an understanding of techniques and receipts for estimation and assessment of the quality of economic models with time-series data.
Course Contents

Course Contents

  • Discrete-time martingale theory.
  • Continuous-time stochastic processes.
  • Stochastic calculus and differential equations.
  • Continuous-time financial models.
Assessment Elements

Assessment Elements

  • non-blocking Homework
  • non-blocking Final exam
  • non-blocking Fall midterm
Interim Assessment

Interim Assessment

  • 2024/2025 2nd module
    0.35 * Fall midterm + 0.4 * Final exam + 0.25 * Homework
Bibliography

Bibliography

Recommended Core Bibliography

  • Enders, W. (2015). Applied Econometric Time Series (Vol. Fourth edition). Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1639192
  • Harvey, A. C. (1993). Time Series Models (Vol. 2nd ed). Cambridge, Mass: MIT Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=11358
  • Mills, T. C., & Markellos, R. N. (2008). The Econometric Modelling of Financial Time Series: Vol. 3rd ed. Cambridge University Press.

Recommended Additional Bibliography

  • Bartoszyński, R., & Niewiadomska-Bugaj, M. (2008). Probability and Statistical Inference (Vol. 2nd ed). Hoboken, N.J.: Wiley-Interscience. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=219782
  • Freund, J. E., Miller, I., & Miller, M. (2014). John E. Freund’s Mathematical Statistics with Applications: Pearson New International Edition (Vol. Eighth edition, Pearson new international edition). Essex, England: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1418305
  • Hogg, R. V., Zimmerman, D. L., & Tanis, E. A. (2015). Probability and Statistical Inference, Global Edition (Vol. Ninth edition. Global edition). Boston: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1419274
  • Larsen, R. J., & Marx, M. L. (2015). An introduction to mathematical statistics and its applications. Slovenia, Europe: Prentice Hall. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.19D77756
  • Lindgren, B. W. (1993). Statistical Theory (Vol. Fourth edition). Boca Raton, Florida: Routledge. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1683924

Authors

  • LUKYANCHENKO PETR PAVLOVICH