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The Kelly Criterion
Kálosi, Szilárd ; Omelka, Marek (advisor) ; Hlávka, Zdeněk (referee)
The present work is devoted to the Kelly criterion, which is a simple method for choosing the amount of the bet for gambles with a positive expected value. In the first part of the work we introduce the mathematical explanation of the criterion, examine the capital after $n$ trials as a function of the bet, the long-run rate of return and asymptotical properties of the capital growth. In the second part we attempt to generalize the Kelly criterion from the first part for some other situations. Examples for a simple game and generalized situations illustrating the properties of the Kelly criterion and results from previous parts compose the last part of the work.
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Penalizační metody ve stochastické optimalizaci
Kálosi, Szilárd ; Branda, Martin (advisor) ; Kaňková, Vlasta (referee)
The submitted thesis studies penalty function methods for stochastic programming problems. The main objective of the paper is to examine penalty function methods for deterministic nonlinear programming, in particular exact penalty function methods, in order to enhance penalty function methods for stochastic programming. For this purpose, the equivalence of the original de- terministic nonlinear and the corresponding penalty function problem using arbi- trary vector norm as the penalty function is shown for convex and invex functions occurring in the problems, respectively. The obtained theorems are consequently applied to multiple chance constrained problems under finite discrete probability distribution to show the asymptotic equivalence of the probabilistic and the cor- responding penalty function problems. The practical use of the newly obtained methods is demonstrated on a numerical study, in which a comparison with other approaches is provided as well. 1
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The Kelly Criterion
Kálosi, Szilárd ; Omelka, Marek (advisor) ; Hlávka, Zdeněk (referee)
The present work is devoted to the Kelly criterion, which is a simple method for choosing the amount of the bet for gambles with a positive expected value. In the first part of the work we introduce the mathematical explanation of the criterion, examine the capital after $n$ trials as a function of the bet, the long-run rate of return and asymptotical properties of the capital growth. In the second part we attempt to generalize the Kelly criterion from the first part for some other situations. Examples for a simple game and generalized situations illustrating the properties of the Kelly criterion and results from previous parts compose the last part of the work.
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