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Performance Analysis Of The Optimal Strategy Under Partial Information

Author

Listed:
  • AHMED BEL HADJ AYED

    (BNP Paribas Global Markets, Paris, France)

  • GRÉGOIRE LOEPER

    (School of Mathematical Sciences, Monash University, Victoria, Australia)

  • SOFIENE EL AOUD

    (Chaire of quantitative finance, laboratory MICS, CentraleSupélec, Châtenay-Malabry, France)

  • FRÉDÉRIC ABERGEL

    (Chaire of quantitative finance, laboratory MICS, CentraleSupélec, Châtenay-Malabry, France)

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 Bel Hadj Ayed & Grégoire Loeper & Sofiene El Aoud & Frédéric Abergel, 2017. "Performance Analysis Of The Optimal Strategy Under Partial Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-21, March.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:02:n:s0219024917500169
    DOI: 10.1142/S0219024917500169
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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. 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.
    4. 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.
    5. Brendle, Simon, 2006. "Portfolio selection under incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 701-723, May.
    6. 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.
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