Open Access
| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 80 | |
| Number of page(s) | 35 | |
| DOI | https://doi.org/10.1051/cocv/2025066 | |
| Published online | 26 September 2025 | |
- M. Huang, R.P. Malhamé and P.E. Caines, Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6 (2006) 221–251. [Google Scholar]
- J.M. Lasry and P.L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
- E. Bayraktar and X. Zhang, Solvability of infinite horizon McKean–Vlasov FBSDEs in mean field control problems and games. Appl. Math. Optim. 87 (2023) Paper No. 13, 26. [Google Scholar]
- A. Bensoussan, S.C.P. Yam and Z. Zhang, Well-posedness of mean-field type forward–backward stochastic differential equations. Stochastic Process. Appl. 125 (2015) 3327–3354. [CrossRef] [MathSciNet] [Google Scholar]
- R. Carmona and F. Delarue, Mean field forward–backward stochastic differential equations. Electron. Commun. Probab. 18 (2013) 15. [Google Scholar]
- R. Carmona and F. Delarue, Forward-backward stochastic differential equations and controlled McKean–Vlasov dynamics. Ann. Probab. 43 (2015) 2647–2700. [CrossRef] [MathSciNet] [Google Scholar]
- R. Tian and Z. Yu, Mean-field type FBSDEs under domination-monotonicity conditions and application to LQ problems. SIAM J. Control Optim. 61 (2023) 22–46. [Google Scholar]
- Q. Wei, J. Yong and Z. Yu, Linear quadratic stochastic optimal control problems with operator coefficients: open-loop solutions. ESAIM Control Optim. Calc. Var. 25 (2019) Paper No. 17, 38. [Google Scholar]
- C. Feng, X. Wang and H. Zhao, Quasi-linear PDEs and forward–backward stochastic differential equations: weak solutions. J. Diff. Equ. 264 (2018) 959–1018. [Google Scholar]
- Z. Wu, B. Xie and Z. Yu, Probabilistic interpretation for a system of quasilinear parabolic partial differential- algebraic equations: the classical solution. Chinese Ann. Math. Ser. B, to appear. [Google Scholar]
- M. Hu, S. Ji and X. Xue, A global stochastic maximum principle for fully coupled forward–backward stochastic systems. SIAM J. Control Optim. 56 (2018) 4309–4335. [CrossRef] [MathSciNet] [Google Scholar]
- P. Briand, B. Delyon, Y. Hu, É. Pardoux and L. Stoica, Lp solutions of backward stochastic differential equations. Stochastic Process. Appl. 108 (2003) 109–129. [CrossRef] [MathSciNet] [Google Scholar]
- R. Buckdahn, Y. Hu and S. Tang, Uniqueness of solution to scalar BSDEs with L exp(μ/2 log(1 + L))-integrable terminal values. Electron. Commun. Probab. 23 (2018) Paper No. 59, 8. [Google Scholar]
- N. El Karoui, S. Peng and M.C. Quenez, Backward stochastic differential equations in finance. Math. Finance 7 (1997) 1–71. [Google Scholar]
- S. Fan and Y. Hu, Existence and uniqueness of solution to scalar BSDEs with L exp(μ/2 log(1 + L))-integrable terminal values: the critical case. Electron. Commun. Probab. 24 (2019) Paper No. 49, 10. [Google Scholar]
- Y. Hu and S. Tang, Existence of solution to scalar BSDEs with L exp(2/λ log(1 + L))-integrable terminal values. Electron. Commun. Probab. 23 (2018) Paper No. 27, 11. [Google Scholar]
- J. Yong, Lp-theory of forward-backward stochastic differential equations. Stochastic Modeling and Control, Banach Center Publ., 122. Warsaw (2020) 255–286. [Google Scholar]
- F. Delarue, On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case. Stochastic Process. Appl. 99 (2002) 209–286. [Google Scholar]
- J. Li and Q. Wei, Optimal control problems of fully coupled FBSDEs and viscosity solutions of Hamilton–Jacobi- Bellman equations. SIAM J. Control Optim. 52 (2014) 1622–1662. [CrossRef] [MathSciNet] [Google Scholar]
- J. Li and Q. Wei, Lp estimates for fully coupled FBSDEs with jumps. Stochastic Process. Appl. 124 (2014) 1582–1611. [Google Scholar]
- B. Xie and Z. Yu, An exploration of Lp-theory for forward–backward stochastic differential equations with random coefficients on small durations. J. Math. Anal. Appl. 483 (2020) 123642, 18. [Google Scholar]
- Q. Meng and S. Yang, Lp estimations of fully coupled FBSDEs. Syst. Control Lett. 172 (2023) Paper No. 105442, 8. [Google Scholar]
- B. Xie and Z. Yu, Lp-estimate for linear forward–backward stochastic differential equations. Acta Math. Sin. (Engl. Ser.) 39 (2023) 827–845. [Google Scholar]
- J. Ma, Z. Wu, D. Zhang and J. Zhang, On well-posedness of forward–backward SDEs – a unified approach. Ann. Appl. Probab. 25 (2015) 2168–2214. [MathSciNet] [Google Scholar]
- Z. Yu, On forward–backward stochastic differential equations in a domination-monotonicity framework. Appl. Math. Optim. 85 (2022) Paper No. 5, 46. [Google Scholar]
- J. Yong, Linear-quadratic optimal control problems for mean-field stochastic differential equations. SIAM J. Control Optim. 51 (2013) 2809–2838. [Google Scholar]
- H. Mei, Q. Wei and J. Yong, Linear-quadratic optimal control problem for mean-field stochastic differential equations with a type of random coefficients. Numer. Algebra Control Optim. 14 (2024) 813–852. [Google Scholar]
- Y. Hu and S. Peng, Solution of forward–backward stochastic differential equations. Probab. Theory Related Fields 103 (1995) 273–283. [CrossRef] [MathSciNet] [Google Scholar]
- S. Peng and Z. Wu, Fully coupled forward–backward stochastic differential equations and applications to optimal control. SIAM J. Control Optim. 37 (1999) 825–843. [CrossRef] [MathSciNet] [Google Scholar]
- J. Yong, Finding adapted solutions of forward–backward stochastic differential equations: method of continuation. Probab. Theory Related Fields 107 (1997) 537–572. [CrossRef] [MathSciNet] [Google Scholar]
- J. Sun, X. Li and J. Yong, Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems. SIAM J. Control Optim. 54 (2016) 2274–2308. [Google Scholar]
- J. Yong and X. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999). [Google Scholar]
- W.M. Wonham, On a matrix Riccati equation of stochastic control. SIAM J. Control 6 (1968) 681–697. [CrossRef] [MathSciNet] [Google Scholar]
- S. Tang, General linear quadratic optimal stochastic control problems with random coefficients: linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim. 42 (2003) 53–75. [CrossRef] [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.
