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Constructing Sublinear Expectations on Path Space

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  • Marcel Nutz
  • Ramon van Handel

Abstract

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that holds without exceptional set. Our results also shed light on the inherent limitations to constructing sublinear expectations through aggregation.

Suggested Citation

  • Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
  • Handle: RePEc:arx:papers:1205.2415
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    File URL: http://arxiv.org/pdf/1205.2415
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    References listed on IDEAS

    as
    1. Marcel Nutz, 2010. "Random G-expectations," Papers 1009.2168, arXiv.org, revised Sep 2013.
    2. Marcel Nutz & H. Mete Soner, 2010. "Superhedging and Dynamic Risk Measures under Volatility Uncertainty," Papers 1011.2958, arXiv.org, revised Jun 2012.
    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.
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    Cited by:

    1. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, revised Sep 2015.
    2. repec:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0344-4 is not listed on IDEAS
    3. Anna Aksamit & Shuoqing Deng & Jan Obl'oj & Xiaolu Tan, 2016. "Robust pricing--hedging duality for American options in discrete time financial markets," Papers 1604.05517, arXiv.org, revised Apr 2017.
    4. Johannes Muhle-Karbe & Marcel Nutz, 2016. "A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing," Papers 1612.09152, arXiv.org, revised Jan 2018.
    5. Bruno Bouchard & Marcel Nutz, 2014. "Consistent Price Systems under Model Uncertainty," Papers 1408.5510, arXiv.org.
    6. Dylan Possamai & Guillaume Royer & Nizar Touzi, 2013. "On the Robust superhedging of measurable claims," Papers 1302.1850, arXiv.org, revised Feb 2013.
    7. repec:spr:joptap:v::y::i::d:10.1007_s10957-018-1230-8 is not listed on IDEAS
    8. Ariel Neufeld & Marcel Nutz, 2012. "Superreplication under Volatility Uncertainty for Measurable Claims," Papers 1208.6486, arXiv.org, revised Apr 2013.
    9. Gordan Zitkovic, 2013. "Dynamic Programming for controlled Markov families: abstractly and over Martingale Measures," Papers 1307.5163, arXiv.org, revised Mar 2014.
    10. Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2014. "A numerical algorithm for a class of BSDEs via the branching process," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1112-1140.
    11. Daniel Bartl, 2016. "Conditional nonlinear expectations," Papers 1612.09103, arXiv.org, revised Nov 2017.
    12. Erhan Bayraktar & Alexander Munk, 2014. "Comparing the $G$-Normal Distribution to its Classical Counterpart," Papers 1407.5139, arXiv.org, revised Dec 2014.
    13. Francesca Biagini & Jacopo Mancin, 2016. "Robust Financial Bubbles," Papers 1602.05471, arXiv.org.
    14. Erhan Bayraktar & Song Yao, 2013. "On the Robust Optimal Stopping Problem," Papers 1301.0091, arXiv.org, revised Apr 2016.
    15. Bruno Bouchard & Marcel Nutz, 2016. "Consistent price systems under model uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 83-98, January.
    16. Marcel Nutz, 2014. "Robust Superhedging with Jumps and Diffusion," Papers 1407.1674, arXiv.org, revised Jul 2015.
    17. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
    18. Bruno Bouchard & Marcel Nutz, 2016. "Consistent price systems under model uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 83-98, January.
    19. Erhan Bayraktar & Xin Zhang & Zhou Zhou, 2018. "Existence of transport plans with domain constraints," Papers 1804.04283, arXiv.org.
    20. Marcel Nutz, 2013. "Utility Maximization under Model Uncertainty in Discrete Time," Papers 1307.3597, arXiv.org.
    21. repec:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-018-0356-8 is not listed on IDEAS
    22. Neufeld, Ariel & Nutz, Marcel, 2014. "Measurability of semimartingale characteristics with respect to the probability law," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3819-3845.
    23. Sigrid Kallblad, 2017. "A Dynamic Programming Principle for Distribution-Constrained Optimal Stopping," Papers 1703.08534, arXiv.org.

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