Mathematics for Economy

Přednášející:

Kateřina Staňková Helisová

Cvičící:

Kateřina Staňková Helisová

Předmět zajišťuje:

katedra matematiky

Anotace:

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.

Požadavky:

Požadavky pro prezenční studium se nacházejí na http://math.feld.cvut.cz/helisova/01mekA1M01MPE.html a pro kombinované studium na http://math.feld.cvut.cz/helisova/01mekAD1M01MPE.html

Osnova přednášek:

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. Random processes - fundamental definitions.

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

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

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

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

10. Technical reserves - indemnity reserve, triangular schemes.

11. Markov chains in bonus systems.

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

13. Cluster analysis - basic definitions.

14. Basic methods of clustering.

Osnova cvičení:

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. Random processes - states classification.

8. Markov chains with discrete time - transition matrix.

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

10. Calculation of premium and reserves in general insurance.

11. Calculation of premium in capital insurance.

12. Calculation of premium in annuity insurance.

13. Basic methods of clustering.

14. Backup

Cíle studia:

Studijní materiály:

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.

Poznámka:

Rozsah výuky v kombinované formě studia: 28p+6s

Rozvrh na zimní semestr 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
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Út	místnost Z4:B2-326 Staňková Helisová K. 09:15–12:30 (přednášková par. 1) Zikova ulice Konzultační místnost místnost Z4:B2-326 Staňková Helisová K. 09:15–10:45 (přednášková par. 1 paralelka 101) Zikova ulice Konzultační místnost
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Rozvrh na letní semestr 2011/2012:

Rozvrh není připraven

Předmět je součástí následujících studijních plánů:

• Electrical Engineering, Power Engineering and Management - Economy and Management of Power Eng. (povinný předmět programu)
• Electrical Engineering, Power Engineering and Management - Economy and Management of Electrical Eng. (povinný předmět programu)