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
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.