Mathematics for Economy
- Department of Mathematics
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 and insurance. At the end of the course, basic procedures of cluster analysis will be presented.
- 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.
- Syllabus of tutorials:
- Study Objective:
- Study materials:
1. Grinstead, Ch.M., Snell, J. L.: Introduction to Probability. American Math. Society, 1997.
2. Ross, S.M.: Stochastic Processes. John Wiley & Sons, 1982.
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.
- Further information:
- 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 - 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)