Subject description - XP01EKM

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XP01EKM Mathematics Models for Economics
Roles:S Extent of teaching:2P+1S
Department:13101 Language of teaching:
Guarantors:Helisová K. Completion:ZK
Lecturers:Helisová K. Credits:4
Tutors:Helisová K. Semester:L


This course is an introduction to the theory of time series and random processes used in economics for describing values (financial assets, product prices, financial loss) randomly developing in time will be shown. Further, the terms of stochastic differential and stochastic integral are introduced.

Study targets:

Presentation of mathematical models used in economy.

Course outlines:

1. Mathematical model of cooperative behavior. Cooperative games and games of strategy.
2. Coalition games. Superadditivty and convexity. Payoffs and solution concepts.
3. Core. Core of a convex game, the characterization by vertices.
4. Iterative projection algorithm for recovering the core elements.
5. Shapley value. Axiomatic derivation. Stochastic intepretation.
6. Applications: market models, cost allocation, voting power.
7. Random processes and time series in economics.
8. Decomposition of time series.
9. Autocorrelative models.
10. Box-Jenkins methodology.
11. Time series in financial mathematics.
12. Random processes as models for evolution of financial assests.
13. Consultation of seminar theses.

Exercises outline:


1. Introduction to the theory of cooperative games. B. Peleg, P. Sudhőlter. Springer, 2007.
2. Principy strategického chování. M. Mareš. UK Praha, Karolinum, 2003. [In Czech]
3. Finanční ekonometrie. T.Cipra. Ekopress, 2007. [In Czech]


Basic knowledge of probability theory.



Coalition game, econometrics, random process, theory of games, time series, Shapley value.

Subject is included into these academic programs:

Program Branch Role Recommended semester
DOKP Common courses S
DOKK Common courses S

Page updated 22.1.2021 09:51:56, semester: Z/2020-1, L/2021-2, L/2020-1, Z/2021-2, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)