State and Control Path-Dependent Stochastic Zero-Sum Differential Games: Viscosity Solutions of Path-Dependent Hamilton–Jacobi–Isaacs Equations
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- El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
- Xu, Changjin & Liu, Zixin & Yao, Lingyun & Aouiti, Chaouki, 2021. "Further exploration on bifurcation of fractional-order six-neuron bi-directional associative memory neural networks with multi-delays," Applied Mathematics and Computation, Elsevier, vol. 410(C).
- Ren, Zhenjie & Tan, Xiaolu, 2017. "On the convergence of monotone schemes for path-dependent PDEs," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1738-1762.
- P. Cardaliaguet & M. Quincampoix, 2008. "Deterministic Differential Games Under Probability Knowledge Of Initial Condition," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 1-16.
- Peter Imkeller & Anthony Réveillac & Jianing Zhang, 2011. "SOLVABILITY AND NUMERICAL SIMULATION OF BSDEs RELATED TO BSPDEs WITH APPLICATIONS TO UTILITY MAXIMIZATION," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(05), pages 635-667.
- R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
- Harald Bauer & Ulrich Rieder, 2005. "Stochastic control problems with delay," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 411-427, December.
- repec:dau:papers:123456789/6046 is not listed on IDEAS
- Yuri F. Saporito & Zhaoyu Zhang, 2020. "PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations," Papers 2003.02035, arXiv.org, revised Apr 2020.
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Keywords
stochastic zero-sum differential games; state and control path-dependent partial differential equations; functional Itô calculus; viscosity solutions; dynamic programming principles;All these keywords.
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