The role of measurability in game-theoretic probability

Vladimir Vovk ()
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Vladimir Vovk: Royal Holloway, University of London

Finance and Stochastics, 2017, vol. 21, issue 3, No 4, 719-739

Abstract: 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.

Keywords: Axiom of choice; Continuous time; Game-theoretic probability; Incomplete markets; Measurability; 91G99; 60G05; 60G25; 60G40; 60G48 (search for similar items in EconPapers)
JEL-codes: C53 G13 G14 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00780-017-0336-4

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