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Dynamic Mean-Variance Optimisation Problems with Deterministic Information

Author

Listed:
  • Martin Schweizer

    (ETH Zurich and Swiss Finance Institute)

  • Danijel Zivoi

    (ETH Zürich)

  • Mario Sikic

    (University of Zurich)

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.

Suggested Citation

  • Martin Schweizer & Danijel Zivoi & Mario Sikic, 2017. "Dynamic Mean-Variance Optimisation Problems with Deterministic Information," Swiss Finance Institute Research Paper Series 17-29, Swiss Finance Institute, revised Feb 2018.
    • Handle: RePEc:chf:rpseri:rp1729
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    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3051199
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    Citations

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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. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.

    More about this item

    Keywords

    Mean-Variance Hedging; Mean-Variance Portfolio Selection; Restricted Information; Partial Information; Deterministic Strategies; Quadratic Optimisation Problems; Nancial Markets; Type (A) Semimartingales;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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