Mathematics for Economy

Lecturer:

Kateřina Staňková Helisová

Tutor:

Kateřina Staňková Helisová

Supervisor:

Department of Mathematics

Synopsis:

Aim of this subject is to give the basic informations about probability, mathematical statistics and Markov chains and to show their applications, mainly in insurance mathematics. At the end of the course, bases of cluster analysis will be shown.

Requirements:

Details are at http://math.feld.cvut.cz/helisova/mekA1M01MPE.html and http://math.feld.cvut.cz/helisova/mekAD1M01MPE.html respectively.

Syllabus of lectures:

1. Random event, definition of probability.

2. Conditional probability, Bayes theorem.

3. Random variable, random vector - density, distribution function, expected value, variance; examples of discrete and continuous distributions.

4. Large numbers laws, central limit theorem.

5. Statistics - parameters estimations, testing of hypotheses.

6. Regression analysis.

7. Random processes - fundamental definitions.

8. Markov chains with discrete time - basic properties, random walk.

9. Markov chains with discrete time - transition matrix, Chapman-Kolmogorov equation, states classification.

10. Markov chains with continuous time - Wiener process, Poisson process.

11. General insurance - basic probability distributions of the number of events and claim amounts.

12. Technical reserves - indemnity reserve, triangular schemes, Markov chains in bonus systems.

13. Life insurance - premium in capital and annuity insurance.

14. Cluster analysis - basic definitions, methods of clustering.

Syllabus of tutorials:

1. Probability of random event.

2. Conditional probability, Bayes theorem.

3. Distribution of random variable.

4. Discrete random variable - distribution function, expected value, variance.

5. Continuous random variable - density, distribution function, expected value, variance.

6. Central limit theorem.

7. Statistics - parameters estimations, testing of hypotheses.

8. Regression analysis.

9. Random processes - stationarity.

10. Markov chains with discrete and continuous time - transition matrix, classification of states, matrix of transition intensity.

11. Calculation of premium and reserves in general insurance.

12. Calculation of premium in capital insurance.

13. Calculation of premium in annuity insurance.

14. Basic methods of clustering.

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.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Elektrotechnika, energetika a management - Ekonomika a řízení energetiky_145106 (compulsory course in the program)
• Elektrotechnika, energetika a management - Ekonomika a řízení elektrotechniky_145126 (compulsory course in the program)