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Some Aspects of Information Theory in Gambling and Economics

  • Hai Q. Dinh
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 200)

Abstract

We discuss applications of information theory to the fields of gambling and economics, such as the problem of gambling on horse races with causal side information, and process of portfolio selection in the stock market. One of the center points is the gambling strategy proposed by Kelly, that, on the one hand, gave a real-life situation of a communication channel without optimum coding in which the rate of transmission is significant. On the other hand, its optimization process opened the door for the theory of rebalanced portfolios with known underlying distributions. We also overview the work on universal portfolios with and without side information, which yield portfolio strategies that have the same exponential rate of growths as the ones achieved by the best state-constant and constant rebalanced portfolios chosen after the stock outcomes are revealed. We do not intend to be encyclopedic, the topics included are bounded to reflect our own research interest.

Keywords

Stock Market Portfolio Selection Forward Error Correction Side Information LDPC Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bell, R., Cover, T.M.: Competitive optimality of logarithmic investment. Math. Oper. Res. 5, 161–166 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bell, R., Cover, T.M.: Game-theoretic optimal portfolios. Manage. Sci. 34, 724–733 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Breiman, L.: Optimal gambling systems for favourable games. In: Berkeley Symposium on Mathematical Statistics and Probability, vol. 4, pp. 65–78 (1961)Google Scholar
  4. 4.
    Berrou, C., Glavieux, A., Thitimajshima, P.: Near Shannon Limit Error-correcting Coding and Decoding: Turbo-codes. In: IEEE Inter. Conf. Comm., pp. 1064–1070 (1993)Google Scholar
  5. 5.
    Cover, T.M.: Universal portfolios. Math. Finance 1, 1–29 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Cover, T.M., Ordentlich, E.: Universal portfolios with side information. IEEE Trans. Inf. Theory 42, 348–363 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Gallager, R.G.: Low Density Parity-Check Codes. MIT Press, Cambridge (1963)Google Scholar
  8. 8.
    Hamming, R.W.: Error detecting and error correcting codes. Bell Sys. Tech. J. 29, 147–160 (1950)MathSciNetGoogle Scholar
  9. 9.
    James, I.: Claude Elwood Shannon 30 April 1916 - 24 February 2001. Biographical Memoirs of Fellows of the Royal Society 55, 257–265 (2009)CrossRefGoogle Scholar
  10. 10.
    Kelly, J.: A new interpretation of information rate. Bell Syst. Tech. J. 35, 917–926 (1956)Google Scholar
  11. 11.
    Kim, Y.-H.: A coding theorem for a class of stationary channels with feedback. IEEE Trans. Inf. Theory. 54, 1488–1499 (2008)CrossRefGoogle Scholar
  12. 12.
    Kramer, G.: Directed information for channels with feedback, Ph.D. Dissertation, Swiss Federal Institute of Technology (ETH), Zurich (1998)Google Scholar
  13. 13.
    Kramer, G.: Capacity results for the discrete memoryless network. IEEE Trans. Inf. Theory 49, 4–21 (2003)zbMATHCrossRefGoogle Scholar
  14. 14.
    Marko, H.: The bidirectional communication theory - a generalization of information theory. IEEE Trans. Comm. 21, 1345–1351 (1973)CrossRefGoogle Scholar
  15. 15.
    Markowitz, H.M.: Portfolio Selection. Journal of Finance 7, 77–91 (1952)Google Scholar
  16. 16.
    Markowitz, H.M.: Portfolio Selection: Efficient Diversification of Investments. John Wiley & Sons, New York (1959)Google Scholar
  17. 17.
    Massey, J.: Causality, feedback and directed information. In: Proc. Int. Symp. Inf. Theory Applic., ISITA 1990 (1990)Google Scholar
  18. 18.
    MIT News, MIT Professor Claude Shannon dies; was founder of digital communications, http://web.mit.edu/newsoffice/2001/shannon.html
  19. 19.
    Pabrai, M.: The Dhandho Investor: The Low-Risk Value Method to High Returns. Willey (2007)Google Scholar
  20. 20.
    Permuter, H.H., Kim, Y.-H., Weissman, T.: On directed information and gambling. CoRR (February 2008)Google Scholar
  21. 21.
    Permuter, H.H., Kim, Y.-H., Weissman, T.: Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing. IEEE Trans. Inform. Theory 57, 3248–3259 (2011)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Permuter, H.H., Weissman, T., Chen, J.: Capacity region of the finite-state multiple-access channel with and without feedback. IEEE Trans. Inf. Theory. 55, 2455–2477 (2009)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Permuter, H.H., Weissman, T., Goldsmith, A.J.: Finite state channels with time-invariant deterministic feedback. IEEE Trans. Inf. Theory. 55, 644–662 (2009)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Peterson, W.W., Brown, D.T.: Cyclic Codes for Error Detection. Proceedings of the IRE 49, 228 (1961)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Shannon, C.E.: A Symbolic Analysis of Relay and Switching Circuits. M.Sc. Thesis, Massachusetts Institute of Technology (1937)Google Scholar
  26. 26.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)Google Scholar
  27. 27.
    Shrader, B., Permuter, H.H.: On the compound finite state channel with feedback. In: Proc. Internat. Symp. Inf. Theory, Nice, France, pp. 396–400 (2007)Google Scholar
  28. 28.
    Tatikonda, S.: Control under communication constraints, Ph.D. disertation, Massachusetts Institute of Technology, Cambridge, MA (2000)Google Scholar
  29. 29.
    Tatikonda, S., Mitter, S.: The capacity of channels with feedback. IEEE Trans. Inf. Theory. 55, 323–349 (2009)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Thorp, E.O.: The Kelly Criterion: Part II. Wilmott Magazine (September 2008)Google Scholar
  31. 31.
    Venkataramanan, R., Pradhan, S.S.: Source coding with feedforward: Rate-distortion theorems and error exponents for a general source. IEEE Trans. Inf. Theory 53, 2154–2179 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesKent State UniversityWarrenUSA

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