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On Mean–Variance Hedging Under Partial Observations And Terminal Wealth Constraints

Author

Listed:
  • VITALII MAKOGIN

    (Institute of Stochastics, Ulm University, D-89069, Ulm, Germany)

  • ALEXANDER MELNIKOV

    (Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, AB T6G 2G1., Canada)

  • YULIYA MISHURA

    (Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska 64, Kyiv, 01601, Ukraine)

Abstract

In this paper, a mean-square minimization problem under terminal wealth constraint with partial observations is studied. The problem is naturally connected to the mean–variance hedging (MVH) problem under incomplete information. A new approach to solving this problem is proposed. The paper provides a solution when the underlying pricing process is a square-integrable semi-martingale. The proposed method for study is based on the martingale representation. In special cases, the Clark–Ocone representation can be used to obtain explicit solutions. The results and the method are illustrated and supported by examples with two correlated geometric Brownian motions.

Suggested Citation

  • Vitalii Makogin & Alexander Melnikov & Yuliya Mishura, 2017. "On Mean–Variance Hedging Under Partial Observations And Terminal Wealth Constraints," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-21, August.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:05:n:s0219024917500315
    DOI: 10.1142/S0219024917500315
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    References listed on IDEAS

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    Cited by:

    1. 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.

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