SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Information Theory, Finance and Statistics - NMSA571
Title in English: Teorie informace ve financích a statistice
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: Mgr. Michal Kupsa
Class: M Mgr. FPM
M Mgr. FPM > Volitelné
M Mgr. PMSE
M Mgr. PMSE > Volitelné
Classification: Mathematics > Financial and Insurance Math., Probability and Statistics
Annotation -
Last update: RNDr. Jitka Zichová, Dr. (25.04.2018)
We present the elements of the Information Theory with the focus on applications in Finance and Statistics. The main part of the course is devoted to the theory of an optimal portfolio strategy for stock markets and the related Kelly's scheme for betting. Smaller part presents the relation between the information theory and Hypothesis Testing.
Aim of the course -
Last update: RNDr. Jitka Zichová, Dr. (23.04.2018)

To present basics of information theory with applicatioms to finance and statistics.

Literature - Czech
Last update: RNDr. Jitka Zichová, Dr. (23.04.2018)

T.M. Cover, J.A.Thomas: Elements of Information Theory, second edition, Wiley and Sons, Inc. (2006)

W.F. Sharpe: Investments, Prentice-Hall (1985)

Teaching methods -
Last update: RNDr. Jitka Zichová, Dr. (23.04.2018)

Lecture.

Requirements to the exam - Czech
Last update: RNDr. Jitka Zichová, Dr. (05.06.2019)

Zkouška je ústní. Požadavky ke zkoušce odpovídají sylabu předmětu v rozsahu, který byl prezentován na přednášce.

Syllabus -
Last update: RNDr. Jitka Zichová, Dr. (23.04.2018)

1. Entropy, mutual information, Kullback-Leibler divergence for random variables

2. Entropy rate for discrete random process with discrete time

3. Kelly's gambling, Gambling and side information, Dependent horse races

4. Hypothesis testing, Chernoff-Stein Lemma, Chernoff information

5. Stock Market, Kuhn-Tucker charakterization of the log-optimal portfolio

6. Asymptotic optimality for the log-optimal portfolio

7. Universal portfolio, finite horizon and horizon-free case

Entry requirements -
Last update: RNDr. Jitka Zichová, Dr. (05.06.2019)

Basics of probability theory, mathematical analysis and linear algebra.

 
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