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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Mathematics for Economy

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Code Completion Credits Range Language
B1B01MEK Z,ZK 5 3P+2S Czech
Lecturer:
Kateřina Helisová (guarantor)
Tutor:
Kateřina Helisová (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

The aim is to introduce the basic theory of probability and statistics, familiarise 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 and insurance. At the end of the course, basic procedures of cluster analysis will be presented.

Requirements:
Syllabus of lectures:

1. Review of the basics of probability - random event, random variable, working with random variables.

2. The importance of some discrete random variables in the economy- Poisson and binomial distribution.

3. Importance of some continuous random variables in the economy- exponential and normal distribution.

4. Application of probability in mathematical statistics- unbiased estimates and basic test statistics.

5. Random processes - basic terms.

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

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

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

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

10. Non-life insurance - basic probability distributions of the number and amount of damages.

11. Technical reserves - triangular diagrams, Markov chains in bonus systems.

12th Life insurance - calculations of capital and annuity insurance.

13th Cluster analysis - basic terms, clustering methods.

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 & Sons, 2001.

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer 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
Mon
Tue
Fri
Thu
roomT2:A4-202a
Helisová K.
11:00–12:30
(lecture parallel1
parallel nr.101)

Dejvice
Ucebna
roomT2:D3-209
Helisová K.
12:45–15:15
(lecture parallel1)
Dejvice
Posluchárna
Fri
The course is a part of the following study plans:
Data valid to 2020-01-23
For updated information see http://bilakniha.cvut.cz/en/predmet5620106.html