Capital process and optimality properties of a Bayesian Skeptic in coin-tossing games

Simple item page
dc.creatorKumon, Masayuki
dc.creatorTakemura, Akimichi
dc.creatorTakeuchi, Kei
dc.date2005-10-31
dc.date2008-09-26
dc.date.accessioned2026-07-07T12:07:17Z
dc.date.available2026-07-07T12:07:17Z
dc.descriptionWe study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital process is lucidly expressed in terms of the past average of Reality's moves. From this it is proved that the Skeptic's Bayesian strategy weakly forces the strong law of large numbers (SLLN) with the convergence rate of O(\sqrt{\log n/n})$ and if Reality violates SLLN then the exponential growth rate of the capital process is very accurately described in terms of the Kullback divergence between the average of Reality's moves when she violates SLLN and the average when she observes SLLN. We also investigate optimality properties associated with Bayesian strategy.
dc.identifierhttps://arxiv.org/abs/math/0510662
dc.identifierhttp://arxiv.org/abs/math/0510662
dc.identifierStochastic Analysis and Applications,26:6,1161-1180,2008
dc.identifierdoi:10.1080/07362990802405646
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208914
dc.subjectStatistics Theory
dc.subjectProbability
dc.subjectTrading and Market Microstructure
dc.subject62M20; 62C10
dc.titleCapital process and optimality properties of a Bayesian Skeptic in coin-tossing games
dc.typetext

Files

Collections

arXiv