Mathematics for Economy
Code  Completion  Credits  Range  Language 

AE1M01MPE  Z,ZK  6  4+2  English 
 Lecturer:
 Tutor:
 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, ChapmanKolmogorov 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] 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:
 http://math.feld.cvut.cz/helisova/01pstimfe.html
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Cybernetics and Robotics  Robotics (elective course)
 Cybernetics and Robotics  Senzors and Instrumention (elective course)
 Cybernetics and Robotics  Systems and Control (elective course)
 Open Informatics  Artificial Intelligence (elective course)
 Open Informatics  Computer Engineering (elective course)
 Open Informatics  Computer Vision and Image Processing (elective course)
 Open Informatics  Computer Graphics and Interaction (elective course)
 Open Informatics  Software Engineering (elective course)
 Communications, Multimedia and Electronics  Wireless Communication (elective course)
 Communications, Multimedia and Electronics  Multimedia Technology (elective course)
 Communications, Multimedia and Electronics  Electronics (elective course)
 Communications, Multimedia and Electronics  Networks of Electronic Communication (elective course)
 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)
 Cybernetics and Robotics  Air and Space Systems (elective course)
 Communications, Multimedia and Electronics  Communication Systems (elective course)
 Open Informatics  New  Software Engineering (elective course)