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.
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.
 Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990.
 Stewart W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press 2009.
 Kaas, R., Goovaerts, M., Dhaene, J., Denuit, M.: Modern actuarial risk theory. Kluwer Academic Publishers, 2004.
 Gerber, H.U.: Life Insurance Mathematics. Springer-Verlag, New York-Berlin-Heidelberg, 1990.
 Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. John Wiley & Sons, 2001.