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A Bound on the Financial Value of Information

In: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE

Author

Listed:
  • ANDREW R. BARRON
  • Thomas M. Cover

Abstract

It will be shown that each bit of information at most doubles the resulting wealth in the general stock market setup. This information bound on the growth of wealth is actually attained for certain probability distributions on the market investigated by Kelly. The bound will be shown to be a special case of the result that the increase in exponential growth of wealth achieved with true knowledge of the stock market distribution F over that achieved with incorrect knowledge G is bounded above by D(F‖G), the entropy of F relative to G.

Suggested Citation

  • ANDREW R. BARRON & Thomas M. Cover, 2011. "A Bound on the Financial Value of Information," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 13, pages 153-156, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814293501_0013
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