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Buy-and-Hold Property for Fully Incomplete Markets when Super-replicating Markovian Claims

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  • Ariel Neufeld

Abstract

We show that when the price process $S$ represents a fully incomplete market, the optimal super-replication of any Markovian claim $g(S_T)$ with $g(\cdot)$ being nonnegative and lower semicontinuous is of buy-and-hold type. Since both (unbounded) stochastic volatility models and rough volatility models are examples of fully incomplete markets, one can interpret the buy-and-hold property when super-replicating Markovian claims as a natural phenomenon in incomplete markets.

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  • Ariel Neufeld, 2017. "Buy-and-Hold Property for Fully Incomplete Markets when Super-replicating Markovian Claims," Papers 1707.01178, arXiv.org, revised Oct 2018.
    • Handle: RePEc:arx:papers:1707.01178
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    References listed on IDEAS

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    Cited by:

    1. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Pathwise superhedging on prediction sets," Finance and Stochastics, Springer, vol. 24(1), pages 215-248, January.
    2. Dolinsky, Yan & Zouari, Jonathan, 2020. "Market delay and G-expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 694-707.
    3. Yannick Limmer & Blanka Horvath, 2023. "Robust Hedging GANs," Papers 2307.02310, arXiv.org.
    4. Peter Bank & Yan Dolinsky, 2020. "A Note on Utility Indifference Pricing with Delayed Information," Papers 2011.05023, arXiv.org, revised Mar 2021.
    5. Jonathan Ansari & Eva Lutkebohmert & Ariel Neufeld & Julian Sester, 2022. "Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information," Papers 2204.01071, arXiv.org, revised Sep 2023.
    6. Erhan Bayraktar & Yan Dolinsky & Jia Guo, 2018. "Continuity of Utility Maximization under Weak Convergence," Papers 1811.01420, arXiv.org, revised Jun 2020.
    7. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2017. "Pathwise superhedging on prediction sets," Papers 1711.02764, arXiv.org, revised Oct 2019.
    8. Ariel Neufeld & Julian Sester, 2021. "Model-free price bounds under dynamic option trading," Papers 2101.01024, arXiv.org, revised Jul 2021.

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