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Dynamic optimal capital growth of diversified investment

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  • Luo Yong
  • Zhu Bo
  • Tang Yong

Abstract

We investigate the problem of dynamic optimal capital growth of diversified investment. A general framework that the trader maximize the expected log utility of long-term growth rate of initial wealth was developed. We show that the trader's fortune will exceed any fixed bound when the fraction is chosen less than critical value. But, if the fraction is larger than that value, ruin is almost sure. In order to maximize wealth, we should choose the optimal fraction at each trade. Empirical results with real financial data show the feasible allocation. The larger the fraction and hence the larger the chance of falling below the desired wealth growth path.

Suggested Citation

  • Luo Yong & Zhu Bo & Tang Yong, 2015. "Dynamic optimal capital growth of diversified investment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 577-588, March.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:3:p:577-588
    DOI: 10.1080/02664763.2014.980783
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    References listed on IDEAS

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    1. Matus Medo & Chi Ho Yeung & Yi-Cheng Zhang, 2008. "How to quantify the influence of correlations on investment diversification," Papers 0805.3397, arXiv.org, revised Feb 2009.
    2. Leonard Maclean & William Ziemba & Yuming Li, 2005. "Time to wealth goals in capital accumulation," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 343-355.
    3. William T. Ziemba & Donald B. Hausch, 2008. "The Dr. Z Betting System in England," World Scientific Book Chapters, in: Donald B Hausch & Victor SY Lo & William T Ziemba (ed.), Efficiency Of Racetrack Betting Markets, chapter 56, pages 567-574, World Scientific Publishing Co. Pte. Ltd..
    4. Medo, Matúš & Pis’mak, Yury M. & Zhang, Yi-Cheng, 2008. "Diversification and limited information in the Kelly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6151-6158.
    5. Medo, Matús & Yeung, Chi Ho & Zhang, Yi-Cheng, 2009. "How to quantify the influence of correlations on investment diversification," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 34-39, March.
    6. Matus Medo & Yury M. Pis'mak & Yi-Cheng Zhang, 2008. "Diversification and limited information in the Kelly game," Papers 0803.1364, arXiv.org, revised Jul 2008.
    7. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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