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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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    References listed on IDEAS

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    1. Marcel Nutz, 2011. "A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations," Papers 1106.3273, arXiv.org, revised May 2012.
    2. Marcel Nutz & H. Mete Soner, 2010. "Superhedging and Dynamic Risk Measures under Volatility Uncertainty," Papers 1011.2958, arXiv.org, revised Jun 2012.
    3. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    4. Song, Yongsheng, 2011. "Properties of hitting times for G-martingales and their applications," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1770-1784, August.
    5. Marcel Nutz, 2010. "Random G-expectations," Papers 1009.2168, arXiv.org, revised Sep 2013.
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