Multistep Bayesian strategy in coin-tossing games and its application to asset trading games in continuous time

摘要

We study multistep Bayesian betting strategies in coin-tossing games in theframework of game-theoretic probability of Shafer and Vovk (2001). We show thatby a countable mixture of these strategies, a gambler or an investor canexploit arbitrary patterns of deviations of nature's moves from independentBernoulli trials. We then apply our scheme to asset trading games in continuoustime and derive the exponential growth rate of the investor's capital when thevariation exponent of the asset price path deviates from two.