Sequential optimizing strategy in multi-dimensional bounded forecasting games

We propose a sequential optimizing betting strategy in the multi dimensional bounded forecasting game in the framework of game-theoretic probability of Shafer and Vovk (2001) [10] By studying the asymptotic behavior of its capital process we prove a generalization of the strong law of large numbers where the convergence rate of the sample mean vector depends on the growth rate of the quadratic variation process The. growth rate of the quadratic variation process may be slower than the number of rounds or may even be zero We also introduce an information criterion for selecting efficient betting items These results art.. then applied to multiple asset trading strategies in discrete time and continuous time games In the case of a continuous time game we present a measure of the jaggedness of a vector valued continuous process Our results are examined by several numerical examples (c) 2010 Elsevier B V All rights reserved