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Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation

Citations

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Cited by:

  1. Song, Yongsheng, 2020. "Normal approximation by Stein’s method under sublinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2838-2850.
  2. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
  3. Lin, Qian, 2019. "Jensen inequality for superlinear expectations," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 79-83.
  4. Hu, Mingshang & Ji, Shaolin, 2017. "Dynamic programming principle for stochastic recursive optimal control problem driven by a G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 107-134.
  5. Laurence Carassus, 2021. "Quasi-sure essential supremum and applications to finance," Papers 2107.12862, arXiv.org, revised Mar 2024.
  6. Xiao, Guanli & Wang, JinRong & O’Regan, Donal, 2020. "Existence, uniqueness and continuous dependence of solutions to conformable stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
  7. 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.
  8. Peter Bank & Yan Dolinsky & Selim Gokay, 2014. "Super-replication with nonlinear transaction costs and volatility uncertainty," Papers 1411.1229, arXiv.org, revised Jun 2015.
  9. Wei Chen, 2013. "G-consistent price system and bid-ask pricing for European contingent claims under Knightian uncertainty," Papers 1308.6256, arXiv.org, revised Sep 2013.
  10. Wentao Hu, 2019. "calculation worst-case Value-at-Risk prediction using empirical data under model uncertainty," Papers 1908.00982, arXiv.org.
  11. Li, Hanwu, 2019. "Optimal stopping under $\textit{G}$-expectation," Center for Mathematical Economics Working Papers 606, Center for Mathematical Economics, Bielefeld University.
  12. Osuka, Emi, 2013. "Girsanov’s formula for G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1301-1318.
  13. Yan Dolinsky & Halil Soner, 2013. "Duality and convergence for binomial markets with friction," Finance and Stochastics, Springer, vol. 17(3), pages 447-475, July.
  14. Ariel Neufeld & Marcel Nutz, 2012. "Superreplication under Volatility Uncertainty for Measurable Claims," Papers 1208.6486, arXiv.org, revised Apr 2013.
  15. 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.
  16. Wei Chen, 2013. "Fractional G-White Noise Theory, Wavelet Decomposition for Fractional G-Brownian Motion, and Bid-Ask Pricing Application to Finance Under Uncertainty," Papers 1306.4070, arXiv.org.
  17. Ren, Yong & Hu, Lanying, 2011. "A note on the stochastic differential equations driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 580-585, May.
  18. Gao, Fuqing, 2009. "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3356-3382, October.
  19. 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.
  20. Shige Peng & Huilin Zhang, 2022. "Wong–Zakai Approximation for Stochastic Differential Equations Driven by G-Brownian Motion," Journal of Theoretical Probability, Springer, vol. 35(1), pages 410-425, March.
  21. Dela Vega, Engel John C. & Elliott, Robert J., 2022. "Backward stochastic differential equations with regime-switching and sublinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 278-298.
  22. 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.
  23. Max Nendel, 2021. "Markov chains under nonlinear expectation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 474-507, January.
  24. Changhong Guo & Shaomei Fang & Yong He, 2023. "A Generalized Stochastic Process: Fractional G-Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-34, March.
  25. Liu, Guomin, 2020. "Exit times for semimartingales under nonlinear expectation," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7338-7362.
  26. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
  27. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, revised Sep 2015.
  28. Zhang, Wei & Jiang, Long, 2021. "Solutions of BSDEs with a kind of non-Lipschitz coefficients driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 171(C).
  29. 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.
  30. Marcel Nutz, 2011. "A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations," Papers 1106.3273, arXiv.org, revised May 2012.
  31. 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.
  32. Nendel, Max, 2018. "Markov Chains under Nonlinear Expectation," Center for Mathematical Economics Working Papers 588, Center for Mathematical Economics, Bielefeld University.
  33. Moreau, Ludovic, 2012. "A contribution in stochastic control applied to finance and insurance," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/10711 edited by Bouchard, Bruno.
  34. Gao, Fuqing & Jiang, Hui, 2010. "Large deviations for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2212-2240, November.
  35. Hanwu Li & Yongsheng Song, 2021. "Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2285-2314, December.
  36. 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.
  37. Hu, Mingshang & Wang, Falei & Zheng, Guoqiang, 2016. "Quasi-continuous random variables and processes under the G-expectation framework," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2367-2387.
  38. 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.
  39. Zhengqi Ma & Shoucheng Yuan & Kexin Meng & Shuli Mei, 2023. "Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
  40. Guomin Liu, 2021. "Girsanov Theorem for G-Brownian Motion: The Degenerate Case," Journal of Theoretical Probability, Springer, vol. 34(1), pages 125-140, March.
  41. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.
  42. Shengqiu Sun, 2022. "Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Coefficients in (y, z)," Journal of Theoretical Probability, Springer, vol. 35(1), pages 370-409, March.
  43. 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.
  44. Nendel, Max & Röckner, Michael, 2019. "Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems," Center for Mathematical Economics Working Papers 618, Center for Mathematical Economics, Bielefeld University.
  45. Marcel Nutz, 2014. "Robust Superhedging with Jumps and Diffusion," Papers 1407.1674, arXiv.org, revised Jul 2015.
  46. Johannes Muhle-Karbe & Marcel Nutz, 2018. "A risk-neutral equilibrium leading to uncertain volatility pricing," Finance and Stochastics, Springer, vol. 22(2), pages 281-295, April.
  47. Johannes Muhle-Karbe & Marcel Nutz, 2016. "A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing," Papers 1612.09152, arXiv.org, revised Jan 2018.
  48. 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.
  49. Xu, Yuhong, 2022. "Optimal growth under model uncertainty," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
  50. 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.
  51. Changhong Guo & Shaomei Fang & Yong He, 2023. "Derivation and Application of Some Fractional Black–Scholes Equations Driven by Fractional G-Brownian Motion," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1681-1705, April.
  52. Bartl, Daniel, 2020. "Conditional nonlinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 785-805.
  53. 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.
  54. Pengju Duan, 2021. "Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control," Mathematics, MDPI, vol. 9(9), pages 1-7, April.
  55. Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
  56. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
  57. Hu, Mingshang & Ji, Xiaojun & Liu, Guomin, 2021. "On the strong Markov property for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 417-453.
  58. Li, Hanwu & Peng, Shige & Soumana Hima, Abdoulaye, 2018. "Reflected Solutions of BSDEs Driven by $\textit{G}$-Brownian Motion," Center for Mathematical Economics Working Papers 590, Center for Mathematical Economics, Bielefeld University.
  59. Yan Dolinsky & Halil Mete Soner, 2011. "Duality and Convergence for Binomial Markets with Friction," Papers 1106.2095, arXiv.org.
  60. Nendel, Max, 2019. "On Nonlinear Expectations and Markov Chains under Model Uncertainty," Center for Mathematical Economics Working Papers 628, Center for Mathematical Economics, Bielefeld University.
  61. Yin, Wensheng & Cao, Jinde, 2021. "On stability of large-scale G-SDEs: A decomposition approach," Applied Mathematics and Computation, Elsevier, vol. 388(C).
  62. Chen, Xiaoyan, 2010. "Dynkin's formula under the G-expectation," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 519-526, March.
  63. Mingshang Hu & Xiaojuan Li, 2014. "Independence Under the $$G$$ -Expectation Framework," Journal of Theoretical Probability, Springer, vol. 27(3), pages 1011-1020, September.
  64. 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.
  65. Felix-Benedikt Liebrich & Max Nendel, 2020. "Separability vs. robustness of Orlicz spaces: financial and economic perspectives," Papers 2009.09007, arXiv.org, revised May 2021.
  66. Marcel Nutz & H. Mete Soner, 2010. "Superhedging and Dynamic Risk Measures under Volatility Uncertainty," Papers 1011.2958, arXiv.org, revised Jun 2012.
  67. Rokhlin, Dmitry B., 2015. "Central limit theorem under uncertain linear transformations," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 191-198.
  68. Peiyu Sun & Dehui Wang & Xili Tan, 2023. "Equivalent Conditions of Complete p-th Moment Convergence for Weighted Sum of ND Random Variables under Sublinear Expectation Space," Mathematics, MDPI, vol. 11(16), pages 1-16, August.
  69. Xu, Jie, 2023. "A deviation inequality for increment of a G-Brownian motion under G-expectation and applications," Statistics & Probability Letters, Elsevier, vol. 198(C).
  70. Denk, Robert & Kupper, Michael & Nendel, Max, 2019. "A Semigroup Approach to Nonlinear Lévy Processes," Center for Mathematical Economics Working Papers 610, Center for Mathematical Economics, Bielefeld University.
  71. 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.
  72. Peter Bank & Yan Dolinsky & Ari-Pekka Perkkiö, 2017. "The scaling limit of superreplication prices with small transaction costs in the multivariate case," Finance and Stochastics, Springer, vol. 21(2), pages 487-508, April.
  73. Shige Peng & Shuzhen Yang & Jianfeng Yao, 2018. "Improving Value-at-Risk prediction under model uncertainty," Papers 1805.03890, arXiv.org, revised Jun 2020.
  74. Ren, Yong & He, Qian & Gu, Yuanfang & Sakthivel, R., 2018. "Mean-square stability of delayed stochastic neural networks with impulsive effects driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 56-66.
  75. Qian Lin, 2015. "Dynamic indifference pricing via the G-expectation," Papers 1503.08628, arXiv.org, revised Sep 2020.
  76. Li, Hanwu & Peng, Shige, 2020. "Reflected backward stochastic differential equation driven by G-Brownian motion with an upper obstacle," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6556-6579.
  77. Erhan Bayraktar & Alexander Munk, 2014. "Comparing the $G$-Normal Distribution to its Classical Counterpart," Papers 1407.5139, arXiv.org, revised Dec 2014.
  78. Sathiyaraj, T. & Fečkan, Michal & Wang, JinRong, 2020. "Null controllability results for stochastic delay systems with delayed perturbation of matrices," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
  79. 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.
  80. Peter Bank & Yan Dolinsky, 2016. "Super-Replication with Fixed Transaction Costs," Papers 1610.09234, arXiv.org, revised Oct 2018.
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