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Measurability of semimartingale characteristics with respect to the probability law

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  • Neufeld, Ariel
  • Nutz, Marcel

Abstract

Given a càdlàg process X on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let Psem be the set of all probability measures P under which X is a semimartingale. We construct processes (BP,C,νP) which are jointly measurable in time, space, and the probability law P, and are versions of the semimartingale characteristics of X under P for each P∈Psem. This result gives a general and unifying answer to measurability questions that arise in the context of quasi-sure analysis and stochastic control under the weak formulation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:11:p:3819-3845
    DOI: 10.1016/j.spa.2014.07.006
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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. Beiglböck, Mathias & Schachermayer, Walter & Veliyev, Bezirgen, 2012. "A short proof of the Doob–Meyer theorem," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1204-1209.
    3. Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
    4. Marcel Nutz & H. Mete Soner, 2010. "Superhedging and Dynamic Risk Measures under Volatility Uncertainty," Papers 1011.2958, arXiv.org, revised Jun 2012.
    5. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
    6. Karandikar, Rajeeva L., 1995. "On pathwise stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 11-18, May.
    7. Dylan Possamai & Guillaume Royer & Nizar Touzi, 2013. "On the Robust superhedging of measurable claims," Papers 1302.1850, arXiv.org, revised Feb 2013.
    8. Ariel Neufeld & Marcel Nutz, 2012. "Superreplication under Volatility Uncertainty for Measurable Claims," Papers 1208.6486, arXiv.org, revised Apr 2013.
    9. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
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    Citations

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    Cited by:

    1. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2021. "Duality theory for robust utility maximisation," Finance and Stochastics, Springer, vol. 25(3), pages 469-503, July.
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    3. Guo, Gaoyue & Tan, Xiaolu & Touzi, Nizar, 2017. "Tightness and duality of martingale transport on the Skorokhod space," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 927-956.
    4. Francesca Biagini & Yinglin Zhang, 2017. "Reduced-form framework under model uncertainty," Papers 1707.04475, arXiv.org, revised Mar 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. Romuald Elie & Emma Hubert & Thibaut Mastrolia & Dylan Possamai, 2019. "Mean-field moral hazard for optimal energy demand response management," Papers 1902.10405, arXiv.org, revised Mar 2020.
    7. Jakv{s}a Cvitani'c & Dylan Possamai & Nizar Touzi, 2014. "Moral Hazard in Dynamic Risk Management," Papers 1406.5852, arXiv.org, revised Mar 2015.
    8. Keller, Christian, 2016. "Viscosity solutions of path-dependent integro-differential equations," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2665-2718.
    9. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2017. "Moral Hazard in Dynamic Risk Management," Management Science, INFORMS, vol. 63(10), pages 3328-3346, October.
    10. Gaoyue Guo & Xiaolu Tan & Nizar Touzi, 2015. "Tightness and duality of martingale transport on the Skorokhod space," Papers 1507.01125, arXiv.org, revised Aug 2016.
    11. Ariel Neufeld & Marcel Nutz, 2015. "Robust Utility Maximization with L\'evy Processes," Papers 1502.05920, arXiv.org, revised Mar 2016.
    12. Emma Hubert & Thibaut Mastrolia & Dylan Possamai & Xavier Warin, 2020. "Incentives, lockdown, and testing: from Thucydides's analysis to the COVID-19 pandemic," Papers 2009.00484, arXiv.org, revised Apr 2022.
    13. Köpfer, Benedikt & Rüschendorf, Ludger, 2023. "Markov projection of semimartingales — Application to comparison results," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 361-386.
    14. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2017. "Pathwise superhedging on prediction sets," Papers 1711.02764, arXiv.org, revised Oct 2019.
    15. Tolulope Fadina & Thorsten Schmidt, 2019. "Default Ambiguity," Risks, MDPI, vol. 7(2), pages 1-17, June.
    16. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
    17. Zongxia Liang & Ming Ma, 2020. "Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1035-1072, July.
    18. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Duality Theory for Robust Utility Maximisation," Papers 2007.08376, arXiv.org, revised Jun 2021.
    19. Denk, Robert & Kupper, Michael & Nendel, Max, 2020. "A semigroup approach to nonlinear Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1616-1642.
    20. Emma Hubert, 2023. "Continuous-time incentives in hierarchies," Finance and Stochastics, Springer, vol. 27(3), pages 605-661, July.
    21. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Pathwise superhedging on prediction sets," Finance and Stochastics, Springer, vol. 24(1), pages 215-248, January.
    22. Emma Hubert, 2020. "Continuous-time incentives in hierarchies," Papers 2007.10758, arXiv.org.
    23. Dylan Possamai & Xiaolu Tan & Chao Zhou, 2015. "Stochastic control for a class of nonlinear kernels and applications," Papers 1510.08439, arXiv.org, revised Jul 2017.
    24. Daniel Bartl & Ariel Neufeld & Kyunghyun Park, 2023. "Sensitivity of robust optimization problems under drift and volatility uncertainty," Papers 2311.11248, arXiv.org.
    25. Tolulope Fadina & Thorsten Schmidt, 2018. "Ambiguity in defaultable term structure models," Papers 1801.10498, arXiv.org, revised Apr 2018.

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