Sufficiency on the Stock Market

It is well-known that there are a number of relations between theoretical finance theory and information theory.Some of these relations are exact and some are approximate. In thi s paper we will explore some of these relations and determine under which conditions the relations are exact. It turns out that portfolio theory always leads to Bregman divergences. The Bregman divergence is only proportional to information divergence in situations that are essentially equal to the t ype of gambling studied by Kelly. This can be related an abstract sufficiency condition.

[1]  Imre Csiszár,et al.  Information Theory and Statistics: A Tutorial , 2004, Found. Trends Commun. Inf. Theory.

[2]  J McCarthy,et al.  MEASURES OF THE VALUE OF INFORMATION. , 1956, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Naftali Tishby,et al.  The Information Bottleneck Revisited or How to Choose a Good Distortion Measure , 2007, 2007 IEEE International Symposium on Information Theory.

[4]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[5]  P. Harremoes.  Proper Scoring and Sufficiency , 2015, 1507.07089.

[6]  Steffen Lauritzen,et al.  PROPER LOCAL SCORING RULES ON DISCRETE SAMPLE SPACES , 2011, 1104.2224.

[7]  Tsachy Weissman,et al.  Information Measures: The Curious Case of the Binary Alphabet , 2014, IEEE Transactions on Information Theory.

[8]  Teck-Cheong Lim,et al.  The center of a convex set , 1981 .

[9]  A. Hendrickson,et al.  Proper Scores for Probability Forecasters , 1971 .