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Optimal Portfolio under Fast Mean-reverting Fractional Stochastic Environment

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  • Jean-Pierre Fouque
  • Ruimeng Hu

Abstract

Empirical studies indicate the existence of long range dependence in the volatility of the underlying asset. This feature can be captured by modeling its return and volatility using functions of a stationary fractional Ornstein--Uhlenbeck (fOU) process with Hurst index $H \in (\frac{1}{2}, 1)$. In this paper, we analyze the nonlinear optimal portfolio allocation problem under this model and in the regime where the fOU process is fast mean-reverting. We first consider the case of power utility, and rigorously give first order approximations of the value and the optimal strategy by a martingale distortion transformation. We also establish the asymptotic optimality in all admissible controls of a zeroth order trading strategy. Then, we extend the discussions to general utility functions using the epsilon-martingale decomposition technique, and we obtain similar asymptotic optimality results within a specific family of admissible strategies.

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  • Jean-Pierre Fouque & Ruimeng Hu, 2017. "Optimal Portfolio under Fast Mean-reverting Fractional Stochastic Environment," Papers 1706.03139, arXiv.org, revised Feb 2018.
    • Handle: RePEc:arx:papers:1706.03139
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    2. Bingyan Han & Hoi Ying Wong, 2019. "Mean-variance portfolio selection under Volterra Heston model," Papers 1904.12442, arXiv.org, revised Jan 2020.
    3. Yiran Liu & Harsha Honnappa & Samy Tindel & Nung Kwan Yip, 2021. "Infinite server queues in a random fast oscillatory environment," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 145-179, June.
    4. Nicole Bauerle & Sascha Desmettre, 2018. "Portfolio Optimization in Fractional and Rough Heston Models," Papers 1809.10716, arXiv.org, revised May 2019.
    5. Josselin Garnier & Knut Solna, 2018. "Optimal hedging under fast-varying stochastic volatility," Papers 1810.08337, arXiv.org, revised Mar 2020.
    6. Eduardo Abi Jaber & Enzo Miller & Huyên Pham, 2021. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Post-Print hal-02877569, HAL.
    7. Bingyan Han & Hoi Ying Wong, 2019. "Time-inconsistency with rough volatility," Papers 1907.11378, arXiv.org, revised Dec 2021.
    8. Eduardo Abi Jaber & Enzo Miller & Huy^en Pham, 2020. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Papers 2006.13539, arXiv.org, revised Jan 2021.
    9. Eduardo Abi Jaber & Enzo Miller & Huyên Pham, 2021. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02877569, HAL.
    10. Han, Bingyan & Wong, Hoi Ying, 2021. "Merton’s portfolio problem under Volterra Heston model," Finance Research Letters, Elsevier, vol. 39(C).
    11. Bingyan Han & Hoi Ying Wong, 2019. "Merton's portfolio problem under Volterra Heston model," Papers 1905.05371, arXiv.org, revised Nov 2019.
    12. Eduardo Abi Jaber & Enzo Miller & Huyên Pham, 2020. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Working Papers hal-02877569, HAL.

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