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Dynamic Mean–Variance Optimization Problems With Deterministic Information

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  • MARTIN SCHWEIZER

    (ETH Zürich, Mathematik, HG G51.2, Rämistrasse 101, CH 8092 Zürich, Switzerland2Swiss Finance Institute, Walchestrasse 9, CH 8006 Zürich, Switzerland)

  • DANIJEL ZIVOI

    (ETH Zürich, Mathematik, HG GO47.2, Rämistrasse 101, CH 8092 Zürich, Switzerland)

  • MARIO ŠIKIĆ

    (Universität Zürich, Center for Finance and Insurance, AND 2.41, Andreasstrasse 15, CH 8050 Zürich, Switzerland)

Abstract

We solve the problems of mean–variance hedging (MVH) and mean–variance portfolio selection (MVPS) under restricted information. We work in a setting where the underlying price process S is a semimartingale, but not adapted to the filtration 𝔾 which models the information available for constructing trading strategies. We choose as 𝔾 = 𝔽det the zero-information filtration and assume that S is a time-dependent affine transformation of a square-integrable martingale. This class of processes includes in particular arithmetic and exponential Lévy models with suitable integrability. We give explicit solutions to the MVH and MVPS problems in this setting, and we show for the Lévy case how they can be expressed in terms of the Lévy triplet. Explicit formulas are obtained for hedging European call options in the Bachelier and Black–Scholes models.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:02:n:s0219024918500115
    DOI: 10.1142/S0219024918500115
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    References listed on IDEAS

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    1. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2015. "The F\"ollmer-Schweizer decomposition under incomplete information," Papers 1511.05465, arXiv.org, revised Mar 2016.
    2. 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.
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    4. Vitalii Makogin & Alexander Melnikov & Yuliya Mishura, 2017. "On mean-variance hedging under partial observations and terminal wealth constraints," Papers 1704.06550, arXiv.org.
    5. Ceci, Claudia & Cretarola, Alessandra & Russo, Francesco, 2014. "BSDEs under partial information and financial applications," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2628-2653.
    6. Martin Schweizer, 1994. "Risk‐Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 327-342, October.
    7. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    8. 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.
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    Cited by:

    1. Peter Bank & Yan Dolinsky, 2020. "A Note on Utility Indifference Pricing with Delayed Information," Papers 2011.05023, arXiv.org, revised Mar 2021.
    2. Yan Dolinsky & Or Zuk, 2023. "Explicit Computations for Delayed Semistatic Hedging," Papers 2308.10550, arXiv.org, revised Sep 2024.
    3. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.

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