On Directed Information and Gambling

Details On Directed Information and Gambling On Directed Information and Gambling

2008-02-11

arxiv.org/abs/0802.1383v1

Computer Science

Information Theory

Scientific paper

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 $I(Y^n \to X^n)$ as the amount of information that $Y^n$ \emph{causally} provides about $X^n$. Extensions to stock market portfolio strategies and data compression with causal side information are also discussed.

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