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Dynamic Conic Finance: Pricing And Hedging In Market Models With Transaction Costs Via Dynamic Coherent Acceptability Indices

Author

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  • TOMASZ R. BIELECKI

    (Department of Applied Mathematics, Illinois Institute of Technology, Chicago, 60616 IL, USA)

  • IGOR CIALENCO

    (Department of Applied Mathematics, Illinois Institute of Technology, Chicago, 60616 IL, USA)

  • ISMAIL IYIGUNLER

    (Department of Applied Mathematics, Illinois Institute of Technology, Chicago, 60616 IL, USA)

  • RODRIGO RODRIGUEZ

    (Department of Applied Mathematics, Illinois Institute of Technology, Chicago, 60616 IL, USA)

Abstract

In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic ask and bid prices of a derivative contract in markets with transaction costs. Based on these results, we derive a representation theorem for the dynamic bid and ask prices in terms of dynamically consistent sequence of sets of probability measures and risk-neutral measures. To illustrate our results, we compute the ask and bid prices of some path-dependent options using the dynamic Gain-Loss Ratio.

Suggested Citation

  • Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler & Rodrigo Rodriguez, 2013. "Dynamic Conic Finance: Pricing And Hedging In Market Models With Transaction Costs Via Dynamic Coherent Acceptability Indices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-36.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:01:n:s0219024913500027
    DOI: 10.1142/S0219024913500027
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    References listed on IDEAS

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    1. Alexander S. Cherny & Dilip B. Madan, 2006. "Pricing and hedging in incomplete markets with coherent risk," Papers math/0605064, arXiv.org.
    2. Tomasz R. Bielecki & Igor Cialenco & Zhao Zhang, 2010. "Dynamic Coherent Acceptability Indices and their Applications to Finance," Papers 1010.4339, arXiv.org, revised May 2011.
    3. Alexander S. Cherny, 2006. "Pricing with coherent risk," Papers math/0605049, arXiv.org.
    4. Takuji Arai & Masaaki Fukasawa, 2011. "Convex risk measures for good deal bounds," Papers 1108.1273, arXiv.org.
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    Citations

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    Cited by:

    1. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    2. Marcin Pitera & Mikl'os R'asonyi, 2023. "Utility-based acceptability indices," Papers 2310.02014, arXiv.org.
    3. Erhan Bayraktar & Gu Wang, 2018. "Quantile Hedging in a semi-static market with model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(2), pages 197-227, April.
    4. Dilip B. Madan, 2016. "Conic Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-42, May.
    5. Righi, Marcelo Brutti, 2024. "Star-shaped acceptability indexes," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 170-181.
    6. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2018. "A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 204-221, February.
    7. Qi Feng & Man Luo & Zhaoyu Zhang, 2021. "Deep Signature FBSDE Algorithm," Papers 2108.10504, arXiv.org, revised Aug 2022.

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