2000 character limit reached
Mean-Field SDEs driven by $G$-Brownian Motion (2401.09113v1)
Published 17 Jan 2024 in math.PR and q-fin.MF
Abstract: We extend the notion of mean-field SDEs to SDEs driven by $G$-Brownian motion. More precisely, we consider a $G$-SDE where the coefficients depend not only on time and the current state but also on the solution as random variable.
- Thomas Augustin “Statistics with Imprecise Probabilities—A Short Survey” In Uncertainty in Engineering: Introduction to Methods and Applications, SpringerBriefs in Statistics Cham: Springer International Publishing, 2022, pp. 67–79 DOI: 10.1007/978-3-030-83640-5_5
- “On the impact of robust statistics on imprecise probability models: A review” In Structural Safety 32.6, Modeling and Analysis of Rare and Imprecise Information, 2010, pp. 358–365 DOI: 10.1016/j.strusafe.2010.06.002
- Francesca Biagini, Georg Bollweg and Katharina Oberpriller “Non-linear affine processes with jumps” Publisher: Probability, Uncertainty and Quantitative Risk In Probability, Uncertainty and Quantitative Risk 8.2, 2023, pp. 235–266 DOI: 10.3934/puqr.2023010
- Karl-Wilhelm Georg Bollweg and Thilo Meyer-Brandis “Mean-Field $G$-SDEs and Associated PDEs”
- “Mean-field stochastic differential equations and associated PDEs” Publisher: Institute of Mathematical Statistics In The Annals of Probability 45.2, 2017, pp. 824–878 DOI: 10.1214/15-AOP1076
- Peter E. Caines, Minyi Huang and Roland P. Malhamé “Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle” Publisher: International Press of Boston In Communications in Information and Systems 6.3, 2006, pp. 221–252 DOI: 10.4310/CIS.2006.v6.n3.a5
- René Carmona, François Delarue and Daniel Lacker “Mean field games with common noise” Publisher: Institute of Mathematical Statistics In The Annals of Probability 44.6, 2016, pp. 3740–3803 DOI: 10.1214/15-AOP1060
- “Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs” arXiv:2312.08331 [math] arXiv, 2023 DOI: 10.48550/arXiv.2312.08331
- Laurent Denis, Mingshang Hu and Shige Peng “Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths” In Potential Analysis 34.2, 2011, pp. 139–161 DOI: 10.1007/s11118-010-9185-x
- Tolulope Fadina, Ariel Neufeld and Thorsten Schmidt “Affine processes under parameter uncertainty” In Probability, Uncertainty and Quantitative Risk 4.1, 2019, pp. 5 DOI: 10.1186/s41546-019-0039-1
- “Jeux à champ moyen. I – Le cas stationnaire” In Comptes Rendus Mathematique 343.9, 2006, pp. 619–625 DOI: 10.1016/j.crma.2006.09.019
- “Jeux à champ moyen. II – Horizon fini et contrôle optimal” In Comptes Rendus Mathematique 343.10, 2006, pp. 679–684 DOI: 10.1016/j.crma.2006.09.018
- “Mean field games” In Japanese Journal of Mathematics 2.1, 2007, pp. 229–260 DOI: 10.1007/s11537-007-0657-8
- “Robust consumption-investment problem under CRRA and CARA utilities with time-varying confidence sets” In Mathematical Finance 30.3, 2020, pp. 1035–1072 DOI: 10.1111/mafi.12217
- “Large investor trading impacts on volatility” In Annales de l’Institut Henri Poincaré C 24.2, 2007, pp. 311–323 DOI: 10.1016/j.anihpc.2005.12.006
- Eva Lütkebohmert, Thorsten Schmidt and Julian Sester “Robust deep hedging” arXiv: 2106.10024, 2021
- Henry P. McKean “A Class of Markov Processes Associated with Nonlinear Parabolic Equations” Publisher: National Academy of Sciences Section: Physical Sciences: Mathematics In Proceedings of the National Academy of Sciences 56.6, 1966, pp. 1907–1911 DOI: 10.1073/pnas.56.6.1907
- “Nonlinear Lévy Processes and their Characteristics” arXiv: 1401.7253 In Transactions of the American Mathematical Society 369.1, 2016, pp. 69–95 DOI: 10.1090/tran/6656
- “Robust Utility Maximization with Lévy Processes” arXiv: 1502.05920, 2016
- Marcel Nutz “Robust superhedging with jumps and diffusion” In Stochastic Processes and their Applications 125.12, 2015, pp. 4543–4555 DOI: 10.1016/j.spa.2015.07.008
- “Constructing sublinear expectations on path space” In Stochastic Processes and their Applications 123.8, 2013, pp. 3100–3121 DOI: 10.1016/j.spa.2013.03.022
- Shige Peng “A New Central Limit Theorem under Sublinear Expectations” arXiv: 0803.2656, 2008 URL: http://arxiv.org/abs/0803.2656
- Shige Peng “Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation” In Stochastic Processes and their Applications 118.12, 2008, pp. 2223–2253 DOI: 10.1016/j.spa.2007.10.015
- Shige Peng “Nonlinear expectations and stochastic calculus under uncertainty: with Robust CLT and G-Brownian motion”, Probability theory and stochastic modelling volume 95 Berlin [Heidelberg]: Springer, 2019 DOI: 10.1007/978-3662-59903-7
- Huyên Pham, Xiaoli Wei and Chao Zhou “Portfolio diversification and model uncertainty: A robust dynamic mean-variance approach” In Mathematical Finance 32.1, 2022, pp. 349–404 DOI: 10.1111/mafi.12320
- Erik Quaeghebeur “Introduction to the Theory of Imprecise Probability” In Uncertainty in Engineering: Introduction to Methods and Applications, SpringerBriefs in Statistics Cham: Springer International Publishing, 2022, pp. 37–50 DOI: 10.1007/978-3-030-83640-5_3
- De Sun, Jiang-Lun Wu and Panyu Wu “On distribution dependent stochastic differential equations driven by $G$-Brownian motion” arXiv:2302.12539 [math] arXiv, 2023 URL: http://arxiv.org/abs/2302.12539
- Shengqiu Sun “Mean-field backward stochastic differential equations driven by G-Brownian motion and related partial differential equations” In Mathematical Methods in the Applied Sciences 43.12, 2020, pp. 7484–7505 DOI: 10.1002/mma.6573
- Andrey A. Vlasov “The Vibrational Properties of an Electron Gas” Publisher: IOP Publishing In Soviet Physics Uspekhi 10.6, 1968, pp. 721 DOI: 10.1070/PU1968v010n06ABEH003709
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.