Mathematics Models for Economics
Code  Completion  Credits  Range 

XP01EKM  ZK  4  2P+1S 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

This course is an introduction to the theory of cooperative games and econometrics. In the first part the mathematical model of a coalition game will be introduced. Two main solution concepts (core and Shapley value) together with their properties and applications will be discussed. In the second part basic models 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.
 Requirements:

Basic knowledge of probability theory.
 Syllabus of lectures:

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.BoxJenkins methodology.
11.Time series in financial mathematics.
12.Random processes as models for evolution of financial assests.
13.Consultation of seminar theses.
 Syllabus of tutorials:
 Study Objective:

Presentation of mathematical models used in economy.
 Study materials:

References
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]
 Note:
 Further information:
 http://math.feld.cvut.cz/helisova/01ekm.html
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Doctoral studies, daily studies (compulsory elective course)
 Doctoral studies, combined studies (compulsory elective course)