Continuous-time trading and emergence of randomness

Abstract

A new definition of events of game-theoretic probability zero in continuous time is proposed and used to prove results suggesting that trading in financial markets results in the emergence of properties usually associated with randomness. This paper concentrates on "qualitative" results, stated in terms of order (or order topology) rather than in terms of the precise values taken by the price processes (assumed continuous).

14 pages; this version: new references and minor corrections

References in corpus (5)

• A tutorial on conformal prediction
• A new formulation of asset trading games in continuous time with essential forcing of variation exponent
• Game-theoretic versions of strong law of large numbers for unbounded variables
• Implications of contrarian and one-sided strategies for the fair-coin game
• Game-theoretic Brownian motion

Cited by in corpus (7)

• Continuous-time trading and the emergence of probability
• A new formulation of asset trading games in continuous time with essential forcing of variation exponent
• Integration with respect to model-free price paths with jumps
• Asymptotics of the truncated variation of model-free price paths and semimartingales with jumps
• Sequential optimizing strategy in multi-dimensional bounded forecasting games
• Multistep Bayesian strategy in coin-tossing games and its application to asset trading games in continuous time
• Continuous-time trading and emergence of volatility