 Sequential optimizing strategy in multi-dimensional bounded forecasting gamesMasayuki Kumon, Akimichi Takemura and Kei Takeuchi Stochastic Processes and their Applications, 2011, vol. 121, issue 1, 155-183 Abstract: 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 are 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. Keywords: Game-theoretic; probability; Holder; exponent; Information; criterion; Kullback-Leibler; divergence; Quadratic; variation; Strong; law; of; large; numbers; Universal; portfolio (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:121:y:2011:i:1:p:155-183 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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