Mathematics for Economy
Code  Completion  Credits  Range  Language 

B1B01MEK  Z,ZK  5  3P+2S  Czech 
 Garant předmětu:
 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. 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. Nonlife 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, 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:
 https://math.fel.cvut.cz/en/people/heliskat/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  Electrical Engineering and Management (compulsory course of the branch)