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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 2020 to 2022
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
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

Opinion survey results Examination dates SS schedule Noticeboard

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: Mgr. Michal Kupsa (21.02.2021)

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.

Course completion requirements -

Last update: Mgr. Michal Kupsa (21.02.2021)

Oral exam with written preparation.

Literature - Czech

Last update: Mgr. Michal Kupsa (18.02.2022)

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

Teaching methods -

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

Lecture.

Requirements to the exam -

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

According to the sylabus and the content of the lecture.

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.