Mathematics for Economy
Code  Completion  Credits  Range  Language 

B1M01MEK  Z,ZK  6  4P+2S  Czech 
 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, PrenticeHall, 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. SpringerVerlag, New YorkBerlinHeidelberg, 1990.
[5] Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. John Wiley & Sons, 2001.
 Note:
 Further information:
 http://math.feld.cvut.cz/helisova/01mekA1M01MPE.html
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Electrical Engineering, Power Engineering and Management  Economy and Management of Power Eng. (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management  Economy and Management of Electrical Eng. (compulsory course in the program)