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Kelly criterion and Bayesian statistics
 Pardubický, Štěpán ; Večeř, Jan (advisor) ; Kalina, Jan (referee)
The classic problem of the investor is the search for profitable investment opportu- nities. But how should an investor behave if he finds such an opportunity? The Kelly criterion, named after the American scientist J.L. Kelly, answers this question. The crite- rion maximises the asymptotic exponential growth rate of capital in repeated bets, which it achieves by maximising the expected value of the logarithmic utility function. The criterion assumes a fixed investor's view of the true probability distribution. In practice, however, it is not clear how this opinion should be formed. In this paper, we combine the Kelly criterion with a Bayesian approach that allows to consider multiple opinions instead of a fixed opinion and let them be validated by the evolution of capital. Finally, we apply the findings to the investor's situation in the binomial market. 1
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