The role of measurability in game-theoretic probability. / Vovk, Vladimir.

In: Finance and Stochastics, Vol. 21, No. 3, 07.2017, p. 719–739.

Research output: Contribution to journalArticlepeer-review




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
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

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