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Mean-Variance Hedging For Partially Observed Drift Processes

Author

Listed:
  • HUYÊN PHAM

    (Laboratoire de Probabilités et Modèles Aléatoires, UFR Mathematiques, Case 7012, Université Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France)

Abstract

We consider the mean-variance hedging when an investor observes just the stock prices. We explain how the theory developed in Gouriéroux, Laurent and Pham (1998) and Rheinländer and Schweizer (1997) can be extended to this framework. We then focus to a diffusion model when drift of stock prices are not observed directly but only through a measurement process. By using filtering techniques, we obtain explicit formulae for optimal mean-variance hedging strategies and for the associated minimal risk. Closed-form expressions are provided in the case of a Bayesian investor and when the stock drift is modelled as a linear Gaussian process.

Suggested Citation

  • Huyên Pham, 2001. "Mean-Variance Hedging For Partially Observed Drift Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 263-284.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:02:n:s0219024901000985
    DOI: 10.1142/S0219024901000985
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    Citations

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    Cited by:

    1. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market -with supplementary contents for stochastic interest rates-," CARF F-Series CARF-F-332, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Martin Schweizer & Danijel Zivoi & Mario Šikić, 2018. "Dynamic Mean–Variance Optimization Problems With Deterministic Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, March.
    3. Andrew Papanicolaou, 2018. "Backward SDEs for Control with Partial Information," Papers 1807.08222, arXiv.org.
    4. Masashi Sekine, 2024. "Mean field equilibrium asset pricing model under partial observation: An exponential quadratic Gaussian approach," Papers 2410.01352, arXiv.org.
    5. Shihao Zhu & Jingtao Shi, 2019. "Optimal Reinsurance and Investment Strategies under Mean-Variance Criteria: Partial and Full Information," Papers 1906.08410, arXiv.org, revised Jun 2020.
    6. M. Mania & R. Tevzadze & T. Toronjadze, 2007. "$L^2$-approximating pricing under restricted information," Papers 0708.4095, arXiv.org.
    7. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market -with supplementary contents for stochastic interest rates-," CIRJE F-Series CIRJE-F-891, CIRJE, Faculty of Economics, University of Tokyo.
    8. Masaaki Fujii & Akihiko Takahashi, 2014. "Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows," CARF F-Series CARF-F-338, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Michael Monoyios, 2010. "Utility-Based Valuation and Hedging of Basis Risk With Partial Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 519-551.
    10. M. Mania & R. Tevzadze & T. Toronjadze, 2007. "Mean-variance Hedging Under Partial Information," Papers math/0703424, arXiv.org.
    11. Covello, D. & Santacroce, M., 2010. "Power utility maximization under partial information: Some convergence results," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2016-2036, September.
    12. Masaaki Fujii & Akihiko Takahashi, 2014. "Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows," CIRJE F-Series CIRJE-F-914, CIRJE, Faculty of Economics, University of Tokyo.
    13. Michael Mania & Marina Santacroce, 2008. "Exponential Utility Maximization under Partial Information," ICER Working Papers - Applied Mathematics Series 24-2008, ICER - International Centre for Economic Research.
    14. Masaaki Fujii & Akihiko Takahashi, 2014. "Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows," CARF F-Series CARF-F-348, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    15. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market," Papers 1306.3359, arXiv.org, revised Nov 2013.
    16. Masaaki Fujii & Akihiko Takahashi, 2014. "Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows," Papers 1401.2314, arXiv.org, revised Jul 2014.
    17. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market," CARF F-Series CARF-F-321, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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