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Dynamic no-good-deal pricing measures and extension theorems for linear operators on L ∞

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  • Jocelyne Bion-Nadal
  • Giulia Nunno

Abstract

In an L ∞ -framework, we present majorant-preserving and sandwich-preserving extension theorems for linear operators. These results are then applied to price systems derived by a reasonable restriction of the class of applicable equivalent martingale measures. Our results prove the existence of a no-good-deal pricing measure for price systems consistent with bounds on the Sharpe ratio. We treat both discrete- and continuous-time market models. Within this study we present definitions of no-good-deal pricing measures that are equivalent to the existing ones and extend them to discrete-time models. We introduce the corresponding version of dynamic no-good-deal pricing measures in the continuous-time setting. Copyright Springer-Verlag 2013

Suggested Citation

  • Jocelyne Bion-Nadal & Giulia Nunno, 2013. "Dynamic no-good-deal pricing measures and extension theorems for linear operators on L ∞," Finance and Stochastics, Springer, vol. 17(3), pages 587-613, July.
    • Handle: RePEc:spr:finsto:v:17:y:2013:i:3:p:587-613
    DOI: 10.1007/s00780-012-0195-y
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    References listed on IDEAS

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    5. Bion-Nadal, Jocelyne, 2009. "Time consistent dynamic risk processes," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 633-654, February.
    6. Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
    7. Jocelyne Bion-Nadal & Magali Kervarec, 2010. "Risk measuring under model uncertainty," Papers 1004.5524, arXiv.org, revised Dec 2010.
    8. Jeremy Staum, 2004. "Fundamental Theorems of Asset Pricing for Good Deal Bounds," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 141-161, April.
    9. Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
    10. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
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    Citations

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    Cited by:

    1. Takuji Arai, 2015. "Good deal bounds with convex constraints," Papers 1506.00396, arXiv.org.
    2. Dirk Becherer & Klebert Kentia, 2017. "Hedging under generalized good-deal bounds and model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 171-214, August.
    3. Maria Arduca & Cosimo Munari, 2020. "Fundamental theorem of asset pricing with acceptable risk in markets with frictions," Papers 2012.08351, arXiv.org, revised Apr 2022.
    4. Takuji Arai, 2016. "Good deal bounds with convex constraints: --- examples and proofs ---," Keio-IES Discussion Paper Series 2016-017, Institute for Economics Studies, Keio University.
    5. Maria Arduca & Cosimo Munari, 2023. "Fundamental theorem of asset pricing with acceptable risk in markets with frictions," Finance and Stochastics, Springer, vol. 27(3), pages 831-862, July.
    6. Patrick Cheridito & Michael Kupper & Ludovic Tangpi, 2016. "Duality formulas for robust pricing and hedging in discrete time," Papers 1602.06177, arXiv.org, revised Sep 2017.
    7. Ludovic Tangpi, 2018. "Efficient hedging under ambiguity in continuous time," Papers 1812.10876, arXiv.org, revised Mar 2019.
    8. Takuji Arai, 2017. "Good Deal Bounds With Convex Constraints," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-15, March.
    9. Dirk Becherer & Klebert Kentia, 2016. "Hedging under generalized good-deal bounds and model uncertainty," Papers 1607.04488, arXiv.org, revised Apr 2017.

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    More about this item

    Keywords

    Price operator; Dynamic risk measure; Extension theorem; Representation theorem; Fundamental theorem; Equivalent martingale measure; Good deal; 46E30; 91B70; G12; G13;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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