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

TL;DR

This paper develops multistep Bayesian betting strategies within a game-theoretic framework, demonstrating their ability to exploit deviations in coin-tossing and asset price patterns, and applies them to continuous-time trading to analyze capital growth.

Contribution

It introduces a countable mixture of multistep Bayesian strategies for coin-tossing games and applies these to asset trading, providing new insights into capital growth under non-standard price variations.

Findings

Strategies can exploit arbitrary deviations from independence in coin-tossing.

Applied to asset trading, the scheme quantifies exponential capital growth.

Results relate asset price variation to investor capital growth.

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.