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On optimal investment with processes of long or negative memory

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  • Huy N. Chau
  • Miklos Rasonyi

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 Frechet-differentiable function of the drift of the price process, provided that this drift lies in a suitable Banach space. We then study optimal investment problems with non-Markovian driving processes. In such models there is no hope to get a formula for the achievable maximal utility. Applying results of the first part of the paper we provide first order expansions for certain problems involving fractional Brownian motion either in the drift or in the volatility. We also point out how asymptotic results can be derived for models with strong mean reversion.

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  • Huy N. Chau & Miklos Rasonyi, 2016. "On optimal investment with processes of long or negative memory," Papers 1608.00768, arXiv.org, revised Mar 2017.
    • Handle: RePEc:arx:papers:1608.00768
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    References listed on IDEAS

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    1. 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.
    2. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
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    7. 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.
    8. Huy N. Chau & Andrea Cosso & Claudio Fontana & Oleksii Mostovyi, 2015. "Optimal investment with intermediate consumption under no unbounded profit with bounded risk," Papers 1509.01672, arXiv.org, revised Jun 2017.
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