No. 1059

Title:

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

Author(s):

Kei, Takeuchi (Emeritus, Graduate School of Economics, University of Tokyo);
Masayuki, Kumon (Risk Analysis Research Center, Institute of Statistical Mathematics);
Akimichi, Takemura (Graduate School of Information Science and Technology, University of Tokyo)

Key words:

Beta-binomial distribution, Holder exponent, Kullback divergence, randomness, risk neutral probability, universal prior.

Abstract:

    We study multistep Bayesian betting strategies in coin-tossing games in the framework of game-theoretic probability of Shafer and Vovk (2001). We show that by a countable mixture of these strategies, a gambler or an investor can exploit arbitrary patterns of deviations of nature's moves from independent Bernoulli trials. We then apply our scheme to asset trading games in continuous time and derive the exponential growth rate of the investor's capital when the variation exponent of the asset price path deviates from two.