IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2102.13574.html
   My bibliography  Save this paper

A conditional version of the second fundamental theorem of asset pricing in discrete time

Author

Listed:
  • Lars Niemann
  • Thorsten Schmidt

Abstract

We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices. Moreover, we characterize attainability and market completeness. We derive a conditional version of the second fundamental theorem of asset pricing, which, surprisingly, is not available up to now. The main tool we use are time consistency properties of dynamic nonlinear expectations, which we apply to the super- and subhedging prices. The results obtained extend existing results in the literature, where the conditional setting is considered in most cases only on finite probability spaces.

Suggested Citation

  • Lars Niemann & Thorsten Schmidt, 2021. "A conditional version of the second fundamental theorem of asset pricing in discrete time," Papers 2102.13574, arXiv.org, revised May 2023.
  • Handle: RePEc:arx:papers:2102.13574
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2102.13574
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    2. Detlefsen, Kai & Scandolo, Giacomo, 2005. "Conditional and dynamic convex risk measures," SFB 649 Discussion Papers 2005-006, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Philippe ARTZNER & Karl-Theodor EISELE & Thorsten SCHMIDT, 2022. "Insurance-Finance Arbitrage," Working Papers of LaRGE Research Center 2022-09, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daniel Bartl, 2016. "Conditional nonlinear expectations," Papers 1612.09103, arXiv.org, revised Mar 2019.
    2. Alessandro Doldi & Marco Frittelli, 2021. "Real-Valued Systemic Risk Measures," Mathematics, MDPI, vol. 9(9), pages 1-24, April.
    3. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2019. "Dynamic risk measures for processes via backward stochastic differential equations," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 43-50.
    4. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    5. Qinyu Wu & Fan Yang & Ping Zhang, 2023. "Conditional generalized quantiles based on expected utility model and equivalent characterization of properties," Papers 2301.12420, arXiv.org.
    6. Fei Sun & Jingchao Li & Jieming Zhou, 2018. "Dynamic risk measures with fluctuation of market volatility under Bochne-Lebesgue space," Papers 1806.01166, arXiv.org, revised Mar 2024.
    7. Leitner Johannes, 2007. "Pricing and hedging with globally and instantaneously vanishing risk," Statistics & Risk Modeling, De Gruyter, vol. 25(4), pages 311-332, October.
    8. Freddy Delbaen & Shige Peng & Emanuela Rosazza Gianin, 2010. "Representation of the penalty term of dynamic concave utilities," Finance and Stochastics, Springer, vol. 14(3), pages 449-472, September.
    9. Tsanakas, Andreas, 2009. "To split or not to split: Capital allocation with convex risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 268-277, April.
    10. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2019. "Time-consistency of risk measures: how strong is such a property?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 287-317, June.
    11. Rudloff, Birgit & Street, Alexandre & Valladão, Davi M., 2014. "Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences," European Journal of Operational Research, Elsevier, vol. 234(3), pages 743-750.
    12. Tomasz R. Bielecki & Igor Cialenco & Shibi Feng, 2018. "A Dynamic Model of Central Counterparty Risk," Papers 1803.02012, arXiv.org.
    13. Jocelyne Bion-Nadal, 2006. "Time Consistent Dynamic Risk Processes, Cadlag Modification," Papers math/0607212, arXiv.org.
    14. Föllmer Hans, 2014. "Spatial risk measures and their local specification: The locally law-invariant case," Statistics & Risk Modeling, De Gruyter, vol. 31(1), pages 79-101, March.
    15. Föllmer Hans & Penner Irina, 2006. "Convex risk measures and the dynamics of their penalty functions," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-36, July.
    16. Geissel Sebastian & Sass Jörn & Seifried Frank Thomas, 2018. "Optimal expected utility risk measures," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 73-87, January.
    17. Chen, Zhiping & Li, Gang & Zhao, Yonggan, 2014. "Time-consistent investment policies in Markovian markets: A case of mean–variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 293-316.
    18. Dan A. Iancu & Marek Petrik & Dharmashankar Subramanian, 2015. "Tight Approximations of Dynamic Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 655-682, March.
    19. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2022. "Convexity and sublinearity of g-expectations," Statistics & Probability Letters, Elsevier, vol. 189(C).
    20. Acciaio, Beatrice & Föllmer, Hans & Penner, Irina, 2012. "Risk assessment for uncertain cash flows: model ambiguity, discounting ambiguity, and the role of bubbles," LSE Research Online Documents on Economics 50118, London School of Economics and Political Science, LSE Library.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2102.13574. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.