On directed information and gambling

We study the problem of gambling in horse races with causal side information and show that Masseypsilas 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 rarr 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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