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Martingale representation theorem for the G-expectation

Citations

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Cited by:

  1. Felix-Benedikt Liebrich & Marco Maggis & Gregor Svindland, 2020. "Model Uncertainty: A Reverse Approach," Papers 2004.06636, arXiv.org, revised Mar 2022.
  2. Patrick Beissner & Frank Riedel, 2018. "Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty," Finance and Stochastics, Springer, vol. 22(3), pages 603-620, July.
  3. Beißner, Patrick, 2013. "Coherent Price Systems and Uncertainty-Neutral Valuation," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 80010, Verein für Socialpolitik / German Economic Association.
  4. Marcel Nutz, 2014. "Robust Superhedging with Jumps and Diffusion," Papers 1407.1674, arXiv.org, revised Jul 2015.
  5. 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.
  6. Peter Bank & Yan Dolinsky & Selim Gokay, 2014. "Super-replication with nonlinear transaction costs and volatility uncertainty," Papers 1411.1229, arXiv.org, revised Jun 2015.
  7. Patrick Beissner & Frank Riedel, 2014. "Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty," Papers 1409.6940, arXiv.org.
  8. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Backward stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 759-784.
  9. Osuka, Emi, 2013. "Girsanov’s formula for G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1301-1318.
  10. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
  11. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
  12. Anastasis Kratsios, 2019. "Partial Uncertainty and Applications to Risk-Averse Valuation," Papers 1909.13610, arXiv.org, revised Oct 2019.
  13. Bruno Bouchard & Marcel Nutz, 2015. "Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions," Post-Print hal-00846830, HAL.
  14. Ariel Neufeld & Marcel Nutz, 2012. "Superreplication under Volatility Uncertainty for Measurable Claims," Papers 1208.6486, arXiv.org, revised Apr 2013.
  15. Falei Wang & Guoqiang Zheng, 2021. "Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Generators," Journal of Theoretical Probability, Springer, vol. 34(2), pages 660-681, June.
  16. Hu, Ying & Tang, Shanjian & Wang, Falei, 2022. "Quadratic G-BSDEs with convex generators and unbounded terminal conditions," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 363-390.
  17. He, Wei, 2024. "Multi-dimensional mean-reflected BSDEs driven by G-Brownian motion with time-varying non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 206(C).
  18. Francesca Biagini & Yinglin Zhang, 2017. "Reduced-form framework under model uncertainty," Papers 1707.04475, arXiv.org, revised Mar 2018.
  19. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
  20. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Comparison theorem, Feynman–Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1170-1195.
  21. Biagini, Francesca & Mancin, Jacopo & Brandis, Thilo Meyer, 2019. "Robust mean–variance hedging via G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1287-1325.
  22. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
  23. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
  24. Liu, Guomin, 2020. "Exit times for semimartingales under nonlinear expectation," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7338-7362.
  25. Marcel Nutz, 2014. "Superreplication under model uncertainty in discrete time," Finance and Stochastics, Springer, vol. 18(4), pages 791-803, October.
  26. Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
  27. Erhan Bayraktar & Alexander Munk, 2014. "An $\alpha$-stable limit theorem under sublinear expectation," Papers 1409.7960, arXiv.org, revised Jun 2016.
  28. Mingshang Hu & Xiaojuan Li, 2014. "Independence Under the $$G$$ -Expectation Framework," Journal of Theoretical Probability, Springer, vol. 27(3), pages 1011-1020, September.
  29. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
  30. Nendel, Max & Riedel, Frank & Schmeck, Maren Diane, 2021. "A decomposition of general premium principles into risk and deviation," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 193-209.
  31. Hu, Mingshang & Wang, Falei, 2021. "Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 139-171.
  32. Matteo Burzoni & Marco Maggis, 2019. "Arbitrage-free modeling under Knightian Uncertainty," Papers 1909.04602, arXiv.org, revised Apr 2020.
  33. Song, Yongsheng, 2019. "Properties of G-martingales with finite variation and the application to G-Sobolev spaces," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2066-2085.
  34. Guo, Xin & Pan, Chen, 2018. "Itô’s calculus under sublinear expectations via regularity of PDEs and rough paths," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1711-1749.
  35. Patrick Beissner, 2019. "Coherent-Price Systems and Uncertainty-Neutral Valuation," Risks, MDPI, vol. 7(3), pages 1-18, September.
  36. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2018. "Dynamic programming approach to principal–agent problems," Finance and Stochastics, Springer, vol. 22(1), pages 1-37, January.
  37. Biagini, Francesca & Mazzon, Andrea & Oberpriller, Katharina, 2023. "Reduced-form framework for multiple ordered default times under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 1-43.
  38. Patrick Beissner, 2017. "Equilibrium prices and trade under ambiguous volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 213-238, August.
  39. Matteo Burzoni & Marco Frittelli & Zhaoxu Hou & Marco Maggis & Jan Obłój, 2019. "Pointwise Arbitrage Pricing Theory in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1034-1057, August.
  40. Ludovic Tangpi, 2018. "Efficient hedging under ambiguity in continuous time," Papers 1812.10876, arXiv.org, revised Mar 2019.
  41. Hu, Ying & Lin, Yiqing & Soumana Hima, Abdoulaye, 2018. "Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3724-3750.
  42. Wang, Bingjun & Yuan, Mingxia, 2019. "Forward-backward stochastic differential equations driven by G-Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 39-47.
  43. Marcel Nutz, 2013. "Utility Maximization under Model Uncertainty in Discrete Time," Papers 1307.3597, arXiv.org.
  44. 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.
  45. Matteo Burzoni & Frank Riedel & H. Mete Soner, 2021. "Viability and Arbitrage Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 89(3), pages 1207-1234, May.
  46. Yan Dolinsky & Jonathan Zouari, 2019. "The Value of Insider Information for Super--Replication with Quadratic Transaction Costs," Papers 1910.09855, arXiv.org, revised Sep 2020.
  47. Francesca Biagini & Jacopo Mancin, 2016. "Robust Financial Bubbles," Papers 1602.05471, arXiv.org.
  48. Akhtari, Bahar & Biagini, Francesca & Mazzon, Andrea & Oberpriller, Katharina, 2023. "Generalized Feynman–Kac formula under volatility uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
  49. Drapeau, Samuel & Heyne, Gregor & Kupper, Michael, 2015. "Minimal supersolutions of BSDEs under volatility uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2895-2909.
  50. Francesca Biagini & Jacopo Mancin & Thilo Meyer Brandis, 2016. "Robust Mean-Variance Hedging via G-Expectation," Papers 1602.05484, arXiv.org, revised Aug 2016.
  51. Bruno Bouchard & Marcel Nutz, 2016. "Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 109-124, February.
  52. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2014. "Universal Arbitrage Aggregator in Discrete Time Markets under Uncertainty," Papers 1407.0948, arXiv.org, revised Feb 2015.
  53. Dolinsky, Yan & Nutz, Marcel & Soner, H. Mete, 2012. "Weak approximation of G-expectations," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 664-675.
  54. Francesca Biagini & Andrea Mazzon & Katharina Oberpriller, 2021. "Reduced-form framework for multiple ordered default times under model uncertainty," Papers 2108.04047, arXiv.org, revised Oct 2022.
  55. Erhan Bayraktar & Alexander Munk, 2014. "Comparing the $G$-Normal Distribution to its Classical Counterpart," Papers 1407.5139, arXiv.org, revised Dec 2014.
  56. Bahar Akhtari & Francesca Biagini & Andrea Mazzon & Katharina Oberpriller, 2020. "Generalized Feynman-Kac Formula under volatility uncertainty," Papers 2012.08163, arXiv.org, revised Nov 2022.
  57. Ren, Liying, 2013. "On representation theorem of sublinear expectation related to G-Lévy process and paths of G-Lévy process," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1301-1310.
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