The role of measurability in game-theoretic probability

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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.
Original languageEnglish
Pages (from-to)719–739
Number of pages21
JournalFinance and Stochastics
Issue number3
Early online date7 Jun 2017
Publication statusPublished - Jul 2017


  • Axiom of Choice
  • Continuous time
  • Game-theoretic probability
  • Incomplete markets
  • Measurability

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