Mathematics for Economy

Course guarantor:

Lecturer:

Tutor:

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.

Requirements:

Syllabus of lectures:

1. Basics of probability - random event, conditional probability, Bayes theorem

2. Random variable - definition, distribution function, basic characteristics of random variables - mean value, variance.

3. Importance of some discrete random variables in economics, Poisson and binomial distribution.

4. Importance of some continuous random variables in economics, exponential and normal distribution.

5. Random vector - definition, description, marginal distribution, covariance and correlation, independence of random variables.

6. Central limit theorem - use for basic calculations, its importance in statistics and economics.

7. Basic concepts in statistics - random sample, sample mean, sample variance, quantile, empirical distribution function, histogram, boxplot.

8. Application of probability in statistics - point and interval estimates, hypothesis testing.

9. Random processes - basic concepts.

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. Regression analysis.

14. Reserve formation - basic probability distribution of the number and amount of claims, triangular schemes, Markov chains in bonus systems.

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] Study materials (extended lecture text, presentations, practice examples) available on the course website, which is linked in Moodle.

Note:

Further information:

https://math.fel.cvut.cz/en/people/heliskat/01mekA1M01MPE.html

No time-table has been prepared for this course

The course is a part of the following study plans:

• Electrical Engineering, Power Engineering and Management - Electrical Engineering and Management (compulsory course of the branch)