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Course, academic year 2023/2024
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Information Theory in Finance and Statistics - NMSA571
Title: Teorie informace ve financích a statistice
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Mgr. Michal Kupsa
Class: M Mgr. PMSE
M Mgr. PMSE > Volitelné
Classification: Mathematics > Financial and Insurance Math., Probability and Statistics
Annotation -
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.
Last update: Zichová Jitka, RNDr., Dr. (25.04.2018)
Aim of the course -

To present basics of information theory with applications to finance and statistics. The core of the course is the mathematical theory with precise definitions and theorems. Proofs are not omitted.

Last update: Kupsa Michal, Mgr. (21.02.2021)
Course completion requirements -

Oral exam with written preparation.

Last update: Kupsa Michal, Mgr. (21.02.2021)
Literature - Czech

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

Last update: Kupsa Michal, Mgr. (18.02.2022)
Teaching methods -

Lecture.

Last update: Zichová Jitka, RNDr., Dr. (23.04.2018)
Requirements to the exam -

According to the sylabus and the content of the lecture.

Last update: Zichová Jitka, RNDr., Dr. (29.10.2019)
Syllabus -

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

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

Basics of probability theory, mathematical analysis and linear algebra.

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