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Performance analysis of the optimal strategy under partial information

Author

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  • Ahmed Belhadjayed

    (FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec)

  • Grégoire Loeper

    (Monash University [Clayton])

  • Sofiene El Aoud

    (FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec)

  • Frédéric Abergel

    (MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec)

Abstract

The question addressed in this paper is the performance of the optimal strategy, and the impact of partial information. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein-Uhlenbeck process. We focus on the optimal strategy with a logarithmic utility function under full or partial information. For both cases, we provide the asymptotic expectation and variance of the logarithmic return as functions of the signal-to-noise ratio and of the trend mean reversion speed. Finally, we compare the asymptotic Sharpe ratios of these strategies in order to quantify the loss of performance due to partial information.

Suggested Citation

  • Ahmed Belhadjayed & Grégoire Loeper & Sofiene El Aoud & Frédéric Abergel, 2017. "Performance analysis of the optimal strategy under partial information," Post-Print hal-01512432, HAL.
    • Handle: RePEc:hal:journl:hal-01512432
    DOI: 10.1142/S0219024917500169
    Note: View the original document on HAL open archive server: https://hal.science/hal-01512432
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    References listed on IDEAS

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    1. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 371-399, April.
    2. Lakner, Peter, 1998. "Optimal trading strategy for an investor: the case of partial information," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 77-97, August.
    3. Ahmed Bel Hadj Ayed & Gr'egoire Loeper & Fr'ed'eric Abergel, 2015. "Forecasting trends with asset prices," Papers 1504.03934, arXiv.org, revised Apr 2015.
    4. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
    5. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    6. Brendle, Simon, 2006. "Portfolio selection under incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 701-723, May.
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