The role of measurability in game-theoretic probability |
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Authors: | Email author" target="_blank">Vladimir?VovkEmail author |
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Institution: | 1.Department of Computer Science,Royal Holloway, University of London,Surrey,UK |
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Abstract: | This paper argues that the requirement of measurability (imposed on trading strategies) is indispensable in continuous-time game-theoretic probability. The necessity of the requirement of measurability in measure theory is demonstrated by results such as the Banach–Tarski paradox and is inherited by measure-theoretic probability. The situation in game-theoretic probability turns out to be somewhat similar in that dropping the requirement of measurability allows a trader in a financial security with a non-trivial price path to become infinitely rich while risking only one monetary unit. |
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