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Random G-expectations

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  • Marcel Nutz

Abstract

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely probabilistic and based on an optimal control formulation with path-dependent control sets.

Suggested Citation

  • Marcel Nutz, 2010. "Random G-expectations," Papers 1009.2168, arXiv.org, revised Sep 2013.
    • Handle: RePEc:arx:papers:1009.2168
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    Citations

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    Cited by:

    1. Fadina, Tolulope & Herzberg, Frederik, 2014. "Weak approximation of G-expectation with discrete state space," Center for Mathematical Economics Working Papers 503, Center for Mathematical Economics, Bielefeld University.
    2. Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999, arXiv.org.
    3. David Criens & Lars Niemann, 2023. "Robust utility maximization with nonlinear continuous semimartingales," Mathematics and Financial Economics, Springer, volume 17, number 5, February.
    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. Francesca Biagini & Katharina Oberpriller, 2020. "Reduced-form setting under model uncertainty with non-linear affine processes," Papers 2006.14307, arXiv.org, revised Jun 2020.
    6. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2017. "Hedging with small uncertainty aversion," Finance and Stochastics, Springer, vol. 21(1), pages 1-64, January.
    7. Marcel Nutz, 2014. "Robust Superhedging with Jumps and Diffusion," Papers 1407.1674, arXiv.org, revised Jul 2015.
    8. Fadina, Tolulope & Herzberg, Frederik, 2015. "Hyperfinite construction of G-expectation," Center for Mathematical Economics Working Papers 540, Center for Mathematical Economics, Bielefeld University.
    9. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
    10. Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
    11. Thibaut Mastrolia & Dylan Possamaï, 2018. "Moral Hazard Under Ambiguity," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 452-500, November.
    12. Julian Holzermann, 2020. "Pricing Interest Rate Derivatives under Volatility Uncertainty," Papers 2003.04606, arXiv.org, revised Nov 2021.
    13. Hansen, Peter G., 2022. "New formulations of ambiguous volatility with an application to optimal dynamic contracting," Journal of Economic Theory, Elsevier, vol. 199(C).
    14. Hölzermann, Julian, 2020. "Pricing Interest Rate Derivatives under Volatility Uncertainty," Center for Mathematical Economics Working Papers 633, Center for Mathematical Economics, Bielefeld University.
    15. Yu-Jui Huang & Adrien Nguyen-Huu, 2018. "Time-consistent stopping under decreasing impatience," Finance and Stochastics, Springer, vol. 22(1), pages 69-95, January.
    16. Gordan Zitkovic, 2013. "Dynamic Programming for controlled Markov families: abstractly and over Martingale Measures," Papers 1307.5163, arXiv.org, revised Mar 2014.
    17. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
    18. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2016. "Hedging with Small Uncertainty Aversion," Papers 1605.06429, arXiv.org.
    19. Tolulope Fadina & Thorsten Schmidt, 2018. "Ambiguity in defaultable term structure models," Papers 1801.10498, arXiv.org, revised Apr 2018.
    20. Daniel Bartl & Ariel Neufeld & Kyunghyun Park, 2023. "Sensitivity of robust optimization problems under drift and volatility uncertainty," Papers 2311.11248, arXiv.org.
    21. Peter G. Hansen, 2021. "New Formulations of Ambiguous Volatility with an Application to Optimal Dynamic Contracting," Papers 2101.12306, arXiv.org.
    22. Erhan Bayraktar & Alexander Munk, 2014. "Comparing the $G$-Normal Distribution to its Classical Counterpart," Papers 1407.5139, arXiv.org, revised Dec 2014.

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