Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing

@article{Permuter2011InterpretationsOD,
  title={Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing},
  author={Haim H. Permuter and Young-Han Kim and Tsachy Weissman},
  journal={IEEE Transactions on Information Theory},
  year={2011},
  volume={57},
  pages={3248-3259}
}
We investigate the role of directed information in portfolio theory, data compression, and statistics with causality constraints. In particular, we show that directed information is an upper bound on the increment in growth rates of optimal portfolios in a stock market due to causal side information. This upper bound is tight for gambling in a horse race, which is an extreme case of stock markets. Directed information also characterizes the value of causal side information in instantaneous… CONTINUE READING
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