On directed information and gambling
Haim Henri Permuter, Young-Han Kim, Tsachy Weissman · 2008
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(Ynrarr Xn) as the amount of information that Yncausally provides about Xn. Extensions to stock market portfolio strategies and data compression with causal side information are also discussed.