On Directed Information and Gambling

2008/02/11 by Permuter, Haim H., Kim, Young-Han, Weissman, Tsachy
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.0802.1383

Abstract

We study the problem of gambling in horse races with causal side information and show that Massey's directed information characterizes the increment in the maximum achievable capital growth rate due to the availability of side information. This result gives a natural interpretation of directed information I(Yⁿ → Xⁿ) as the amount of information that Yⁿ causally provides about Xⁿ. Extensions to stock market portfolio strategies and data compression with causal side information are also discussed.

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