On Directed Information and Gambling

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 Xn ) as the amount of information that Y n causally provides about Xn . Extensions to stock market portfolio strategies and data compression with causal side information are also discussed.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Haim H. Permuter, Young-Han Kim, Tsachy Weissman
• Keywords: CORR 2008, Education, Information, Market Portfolio Strategies, Maximum Achievable Capital