Capital Process and Optimality Properties of a Bayesian Skeptic in Coin-Tossing Games

DOI10.1080/07362990802405646zbMath1154.62078arXivmath/0510662OpenAlexW3100232795MaRDI QIDQ3548434

Kei Takeuchi, Masayuki Kumon, Akimichi Takemura

Publication date: 12 December 2008

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510662

zbMATH Keywords

exchangeabilityprior distributionKullback divergencegame-theoretic probabilityhypergeometric distributionbeta-binomial distributionAzuma-Hoeffding-Bennett inequality

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Applications of statistics to actuarial sciences and financial mathematics (62P05) Bayesian problems; characterization of Bayes procedures (62C10) Other game-theoretic models (91A40) Stochastic games, stochastic differential games (91A15)

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A new formulation of asset trading games in continuous time with essential forcing of variation exponent ⋮ Sequential optimizing strategy in multi-dimensional bounded forecasting games ⋮ Exponential inequalities and the law of the iterated logarithm in the unbounded forecasting game ⋮ Gibbs distribution from sequentially predictive form of the second law ⋮ Implications of contrarian and one-sided strategies for the fair-coin game ⋮ An exponential inequality and the convergence rate of the strong law of large numbers in the unbounded forecasting game ⋮ Bayesian Logistic Betting Strategy Against Probability Forecasting ⋮ Continuous-time trading and the emergence of probability ⋮ Multistep Bayesian Strategy in Coin-Tossing Games and Its Application to Asset Trading Games in Continuous Time ⋮ On a simple strategy weakly forcing the strong law of large numbers in the bounded forecasting game

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