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International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 498050, 8 pages
Research Article

Optimal Geometric Mean Returns of Stocks and Their Options

Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA

Received 23 October 2012; Accepted 9 December 2012

Academic Editor: Qing Zhang

Copyright © 2012 Guoyi Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. L. Kelly Jr, “A new interpretation of information rate,” The Bell System Technical Journal, vol. 35, pp. 917–926, 1956. View at MathSciNet
  2. H. Latane, “Criteria for choice among risky ventures,” Journal of Political Economy, vol. 67, no. 2, pp. 144–155, 1959. View at Publisher · View at Google Scholar
  3. H. Latane and D. Tuttle, “Criteria for portfolio building,” Journal of Finance, vol. 22, no. 3, pp. 359–373, 1967.
  4. S. Bickel, “Minimum variance and optimal asymptotic portfolios,” Management Science, vol. 16, no. 3, pp. 221–226, 1969.
  5. J. H. V. Weide, D. W. Peterson, and S. F. Maier, “A strategy which maximizes the geometric mean return on portfolio investments,” Management Science, vol. 23, no. 10, pp. 1117–1123, 1977. View at MathSciNet
  6. S. F. Maier, D. W. Peterson, and J. H. V. Weide, “A monte carlo investigation of characteristics of optimal geometric mean portfolios,” The Journal of Financial and Quantitative Analysis, vol. 12, no. 2, pp. 215–233, 1977.
  7. W. Ziemba, “Note on optimal growth portfolios when yields are serially correlated,” Journal of Financial and Quantitative Analysis, vol. 7, no. 4, pp. 1995–2000, 1972.
  8. E. Elton and M. Gruber, “On the maximization of the geometric mean with lognormal return distribution,” Management Science, vol. 21, no. 4, pp. 483–488, 1974.
  9. W. Bernstein and D. Wilkinson, “Diversification, rebalancing, and the geometric mean frontier,” Social Science Research Network, Working Paper Series, 1997, http://ssrn.com/abstract=53503.
  10. J. Estrada, “Geometric mean maximization: an overlooked portfolio approach?” Journal of Investing, vol. 19, no. 4, pp. 134–147, 20102010.
  11. R. C. Merton, “Optimum consumption and portfolio rules in a continuous-time model,” Journal of Economic Theory, vol. 3, no. 4, pp. 373–413, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. R. McEnally, “Latanes bequest: the best of portfolio strategies,” Journal of Portfolio Management, vol. 12, pp. 21–30, 1986.
  13. L. MacLean, W. Ziemba, and G. Blazenko, “Growth versus security in dynamic investment analysis,” Management Science, vol. 38, no. 11, pp. 1562–1585, 1992.
  14. J. C. Cox, S. A. Ross, and M. Rubinstein, “Option pricing: a simplified approach,” Journal of Financial Economics, vol. 7, no. 3, pp. 229–263, 1979. View at Scopus
  15. F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy, vol. 81, no. 3, pp. 637–654, 1973.