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On optimal investment with processes of long or negative memory

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  • Chau, Huy N.
  • Rásonyi, Miklós

Abstract

We consider the problem of utility maximization for investors with power utility functions. Building on the earlier work Larsen et al. (2016), we prove that the value of the problem is a Fréchet-differentiable function of the drift of the price process, provided that this drift lies in a suitable Banach space.

Suggested Citation

  • Chau, Huy N. & Rásonyi, Miklós, 2018. "On optimal investment with processes of long or negative memory," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1095-1113.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:4:p:1095-1113
    DOI: 10.1016/j.spa.2017.07.006
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    References listed on IDEAS

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    1. Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1642-1662, November.
    2. Paolo Guasoni, 2006. "Asymmetric Information in Fads Models," Finance and Stochastics, Springer, vol. 10(2), pages 159-177, April.
    3. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    4. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    5. Kasper Larsen & Oleksii Mostovyi & Gordan v{Z}itkovi'c, 2014. "An expansion in the model space in the context of utility maximization," Papers 1410.0946, arXiv.org, revised Aug 2016.
    6. S. Gerhold & J. Muhle-Karbe & W. Schachermayer, 2013. "The dual optimizer for the growth-optimal portfolio under transaction costs," Finance and Stochastics, Springer, vol. 17(2), pages 325-354, April.
    7. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
    8. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    9. Paolo Guasoni, 2006. "Asymmetric Information in Fads Models," Finance and Stochastics, Springer, vol. 10(2), pages 159-177, April.
    10. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    11. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    12. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, vol. 18(1), pages 1-37, January.
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    Cited by:

    1. Oleksii Mostovyi & Mihai Sîrbu, 2019. "Sensitivity analysis of the utility maximisation problem with respect to model perturbations," Finance and Stochastics, Springer, vol. 23(3), pages 595-640, July.

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