CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Mathematics for Economy

Code Completion Credits Range Language
BE1M01MEK Z,ZK 6 4P+2S English
Lecturer:
Kateřina Helisová (guarantor)
Tutor:
Kateřina Helisová (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

The aim is to recall the introduction to probability, familiarize students with basic terms properties and methods used in working with random processes, especially with Markov chains, and show applications of these mathematical tools in economics.

Requirements:
Syllabus of lectures:

1. Review of the basics of probability.

2. Random event.

3. Conditional probability, Bayes theorem.

4. Random variable, working with random variables.

5. Basic discrete random variables used in the economy (Poisson and binomial distribution).

6. Basic continuous random variables in the economy (exponential and normal distribution).

7. Application of probability in mathematical statistics - unbiased estimates and maximum likelihood method.

8. Application of probability in mathematical statistics - basic test statistics and hypotheses testing.

9. Random processes - basic terms.

10. Markov chains with discrete time - properties, transition probability matrix, classification of states.

11. Markov chains with continuous time - properties, transition probability matrix, classification of states.

12. Practical use of random processes - Wiener process, Poisson process, applications.

13. Stochastic integral, stochastic differential and their applications in finance.

14. Reserve

Syllabus of tutorials:
Study Objective:
Study materials:

[1] Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990.

[2] Stewart W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press 2009.

[3] Kaas, R., Goovaerts, M., Dhaene, J., Denuit, M.: Modern actuarial risk theory. Kluwer Academic Publishers, 2004.

[4] Gerber, H.U.: Life Insurance Mathematics. Springer-Verlag, New York-Berlin-Heidelberg, 1990.

[5] Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. John Wiley &amp; Sons, 2001.

Note:
Further information:
http://math.feld.cvut.cz/helisova/01pstimfe.html
Time-table for winter semester 2019/2020:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomT2:C4-78Helisová K.12:45–14:15(lecture parallel1)DejviceT2:C4-78roomT2:C4-78Helisová K.16:15–17:45(lecture parallel1parallel nr.101)DejviceT2:C4-78 roomT2:C4-78Helisová K.14:30–16:00(lecture parallel1)DejviceT2:C4-78
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-08-09
For updated information see http://bilakniha.cvut.cz/en/predmet4863506.html