Kellyho kritérium a Bayesovská statistika
| Thesis title in Czech: | Kellyho kritérium a Bayesovská statistika |
|---|---|
| Thesis title in English: | Kelly criterion and Bayesian statistics |
| Key words: | Kellyho kritérium|Bayesovská statistika|Binomický trh |
| English key words: | Kelly criterion|Bayesian statistics|Binomial market |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | čeština |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. RNDr. Jan Večeř, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 19.07.2022 |
| Date of assignment: | 19.07.2022 |
| Confirmed by Study dept. on: | 27.07.2022 |
| Date and time of defence: | 26.06.2023 09:00 |
| Date of electronic submission: | 10.05.2023 |
| Date of submission of printed version: | 15.05.2023 |
| Date of proceeded defence: | 26.06.2023 |
| Opponents: | RNDr. Jan Kalina, Ph.D. |
| Guidelines |
| Kelly criterion describes optimal trading strategy in terms of the fraction of wealth being invested in a binary random variable in the case that the probabilistic views of the agent and the market differ. Traditional literature assumes that the probabilistic view of the agent is fixed in given, however in practice it is not clear how this opinion should be created. A modern statistical approach is to consider all possible models for the parameter "p" of success of the random variable and have this parameter be validated by observed data. The goal of this thesis is to:
1) State the Kelly criterion as a question of constrained optimization and show connections to hypothesis testing (based on the optimal solution in the form of a likelihood ratio) and information theory (optimal expected utility is related to the relative entropy). 2) Study limiting behavior of the wealth process in this classical setup. 3) Apply the Bayesian approach, meaning start with all possible values of "p", where the initial weights correspond to the prior distribution. 4) Study limiting behavior of the wealth process in the Bayesian setup. 5) In the classical binomial model of the stock evolution, show that the price of the stock is proportional to the likelihood ratio of the two asset measures. 6) Study limiting behavior of the binomial model when the agents trading in both underlying asset are performing the Bayesian update. |
| References |
| Browne, Sid, and Ward Whitt. "Portfolio choice and the Bayesian Kelly criterion." Advances in Applied Probability 28.4 (1996): 1145-1176.
Vecer, Jan. "Stochastic Finance: A Numeraire Approach", CRC Press, 2011. |