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Optimal Investment Strategy for Risky Assets

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  • Sergei Maslov
  • Yi-Cheng Zhang

Abstract

We design an optimal strategy for investment in a portfolio of assets subject to a multiplicative Brownian motion. The strategy provides the maximal typical long-term growth rate of investor's capital. We determine the optimal fraction of capital that an investor should keep in risky assets as well as weights of different assets in an optimal portfolio. In this approach both average return and volatility of an asset are relevant indicators determining its optimal weight. Our results are particularly relevant for very risky assets when traditional continuous-time Gaussian portfolio theories are no longer applicable.

Suggested Citation

  • Sergei Maslov & Yi-Cheng Zhang, 1998. "Optimal Investment Strategy for Risky Assets," Papers cond-mat/9801240, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/9801240
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    Cited by:

    1. Edward W. Piotrowski, "undated". "Problems with the Astumian's Paradox (in Polish)," Departmental Working Papers 121pl, University of Bialtystok, Department of Theoretical Physics.
    2. J. Emeterio Navarro-Barrientos & Frank E. Walter & Frank Schweitzer, 2008. "Risk-Seeking Versus Risk-Avoiding Investments In Noisy Periodic Environments," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 971-994.
    3. Arpan Jani, 2021. "An agent-based model of repeated decision making under risk: modeling the role of alternate reference points and risk behavior on long-run outcomes," Journal of Business Economics, Springer, vol. 91(9), pages 1271-1297, November.
    4. Navarro-Barrientos, Jesús Emeterio & Cantero-Álvarez, Rubén & Matias Rodrigues, João F. & Schweitzer, Frank, 2008. "Investments in random environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2035-2046.
    5. E. Aurell & R. Baviera & O. Hammarlid & M. Serva & A. Vulpiani, 1998. "A general methodology to price and hedge derivatives in incomplete markets," Papers cond-mat/9810257, arXiv.org, revised Apr 1999.
    6. Rubina Zadourian, 2024. "Model-based and empirical analyses of stochastic fluctuations in economy and finance," Papers 2408.16010, arXiv.org.
    7. Subbiah, Mohan & Fabozzi, Frank J., 2016. "Hedge fund allocation: Evaluating parametric and nonparametric forecasts using alternative portfolio construction techniques," International Review of Financial Analysis, Elsevier, vol. 45(C), pages 189-201.
    8. Sornette, Didier, 1998. "Large deviations and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 251-283.
    9. E. Aurell & P. Muratore-Ginanneschi, 2002. "Growth-Optimal Strategies with Quadratic Friction Over Finite-Time Investment Horizons," Papers cond-mat/0211044, arXiv.org.
    10. Paolo Laureti & Matus Medo & Yi-Cheng Zhang, 2010. "Analysis of Kelly-optimal portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 689-697.
    11. Chung-Han Hsieh, 2021. "On Asymptotic Log-Optimal Buy-and-Hold Strategy," Papers 2103.04898, arXiv.org.
    12. Erik Aurell & Paolo Muratore-Ginanneschi, 1999. "Financial Friction and Multiplicative Markov Market Game," Papers cond-mat/9908253, arXiv.org.
    13. Hendrik J. Blok, 2000. "On the nature of the stock market: Simulations and experiments," Papers cond-mat/0010211, arXiv.org.

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