Ma, Tianfu; Xu, Juanjuan; Zhang, Huanshui Explicit solution to delayed forward and backward stochastic differential equations. (English) Zbl 1544.93314 Int. J. Syst. Sci., Princ. Appl. Syst. Integr. 55, No. 10, 2144-2153 (2024). MSC: 93C23 34K50 93C05 49N10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhang, Shuaiqi; Chen, Zhen-Qing Fully coupled forward-backward stochastic differential equations driven by sub-diffusions. (English) Zbl 07901389 J. Differ. Equations 405, 337-358 (2024). MSC: 60K50 60H10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ji, Shaolin; Liu, Haodong Solvability of one kind of forward-backward stochastic difference equations. (English) Zbl 07887794 Commun. Stat., Theory Methods 53, No. 16, 5853-5870 (2024). MSC: 62-XX × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Deng, Chao; Su, Xizhi; Zhou, Chao Relative wealth concerns with partial information and heterogeneous priors. (English) Zbl 1537.91282 SIAM J. Financ. Math. 15, No. 2, 360-398 (2024). MSC: 91G10 60H30 91A80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Xu, Maozhong; Tang, Maoning; Meng, Qingxin Forward-backward stochastic evolution equations in infinite dimensions and application to LQ optimal control problems. (English) Zbl 1537.93337 Syst. Control Lett. 185, Article ID 105748, 11 p. (2024). MSC: 93C15 60H10 93C35 49N10 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Na; Wang, Shujun Linear-quadratic stochastic Stackelberg games of \(N\) players for time-delay systems and related FBSDEs. (English) Zbl 1536.91043 Appl. Math. Optim. 89, No. 3, Paper No. 67, 47 p. (2024). MSC: 91A15 91A65 91A06 49N10 × Cite Format Result Cite Review PDF Full Text: DOI
Kyong-Il, Ri; Myong-Guk, Sin Existence and uniqueness of solution for fully coupled fractional forward-backward stochastic differential equations with delay and anticipated term. (English) Zbl 1534.34074 Stat. Probab. Lett. 206, Article ID 109954, 9 p. (2024). MSC: 34K37 34K50 60G22 × Cite Format Result Cite Review PDF Full Text: DOI
Rolón Gutiérrez, Esteban J.; Nguyen, Son Luu; Yin, George Markovian-switching systems: backward and forward-backward stochastic differential equations, mean-field interactions, and nonzero-sum differential games. (English) Zbl 1539.60088 Appl. Math. Optim. 89, No. 2, Paper No. 33, 47 p. (2024). Reviewer: Anatoliy Swishchuk (Calgary) MSC: 60J25 60J27 60J60 93E20 × Cite Format Result Cite Review PDF Full Text: DOI
Wu, Zhen; Zhang, Detao Theory of forward backward stochastic differential equations and its applications. (Chinese. English summary) Zbl 1538.60105 Chin. J. Appl. Probab. Stat. 39, No. 3, 413-435 (2023). MSC: 60H10 60H05 60H20 60H30 93E03 × Cite Format Result Cite Review PDF Full Text: Link
Huang, Jianhui; Li, Wenqiang; Zhao, Hanyu A class of optimal control problems of forward-backward systems with input constraint. (English) Zbl 1536.49007 J. Optim. Theory Appl. 199, No. 3, 1050-1084 (2023). MSC: 49J20 49N80 × Cite Format Result Cite Review PDF Full Text: DOI
Hu, Kaitong; Ren, Zhenjie; Touzi, Nizar On path-dependent multidimensional forward-backward SDEs. (English) Zbl 1515.60194 Numer. Algebra Control Optim. 13, No. 3-4, 413-430 (2023). MSC: 60H10 60H15 60H30 35R60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Yong, Jiongmin Forward-backward stochastic differential equations: initiation, development and beyond. (English) Zbl 1515.60227 Numer. Algebra Control Optim. 13, No. 3-4, 367-391 (2023). MSC: 60H10 60H15 60H35 93E20 35K40 × Cite Format Result Cite Review PDF Full Text: DOI
Chen, Yanbo; Nie, Tianyang; Wang, Shujun Fully-coupled mean-field FBSDE and maximum principle for related optimal control problem. (English) Zbl 1539.93201 Syst. Control Lett. 177, Article ID 105550, 15 p. (2023). MSC: 93E20 60H30 91A23 91A65 49N70 × Cite Format Result Cite Review PDF Full Text: DOI
Xie, Bing; Yu, Zhi Yong \(L^p\)-estimate for linear forward-backward stochastic differential equations. (English) Zbl 1521.60026 Acta Math. Sin., Engl. Ser. 39, No. 5, 827-845 (2023). Reviewer: Hossam A. Ghany (al-Qāhira) MSC: 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Bayraktar, Erhan; Wu, Ruoyu; Zhang, Xin Propagation of chaos of forward-backward stochastic differential equations with graphon interactions. (English) Zbl 1520.91047 Appl. Math. Optim. 88, No. 1, Paper No. 25, 44 p. (2023). MSC: 91A16 60H30 91A06 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tsuchiya, Takahiro Fully coupled drift-less forward and backward stochastic differential equations in a degenerate case. (English) Zbl 1515.60216 Japan J. Ind. Appl. Math. 40, No. 2, 1031-1051 (2023). MSC: 60H10 60H30 35A02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Meng, Qingxin; Yang, Shuzhen \( L^p\) estimations of fully coupled FBSDEs. (English) Zbl 1516.93275 Syst. Control Lett. 172, Article ID 105442, 8 p. (2023). MSC: 93E20 49N10 60H30 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Li, Xiaojuan Forward-backward stochastic differential equations driven by \(G\)-Brownian motion under weakly coupling condition. (English) Zbl 1533.60091 J. Math. Anal. Appl. 526, No. 1, Article ID 127274, 19 p. (2023). MSC: 60H10 60G65 60H30 91G20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wu, Zhen; Xie, Bing; Yu, Zhiyong Sobolev space weak solutions to one kind of quasilinear parabolic partial differential equations related to forward-backward stochastic differential equations. (English) Zbl 1528.60063 Discrete Contin. Dyn. Syst. 43, No. 6, 2494-2523 (2023). MSC: 60H10 35K55 35C05 × Cite Format Result Cite Review PDF Full Text: DOI
Aman, Auguste; Coulibaly, Harouna; Đorđević, Jasmina Forward-backward stochastic differential equations with delay generators. (English) Zbl 1523.60095 Stoch. Dyn. 23, No. 2, Article ID 2350012, 14 p. (2023). MSC: 60H10 60F10 60H30 × Cite Format Result Cite Review PDF Full Text: DOI
Huang, Pengyan; Wang, Guangchen; Wang, Wencan; Wang, Yu A linear-quadratic mean-field game of backward stochastic differential equation with partial information and common noise. (English) Zbl 1511.91015 Appl. Math. Comput. 446, Article ID 127899, 17 p. (2023). MSC: 91A16 93E20 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Tian, Ran; Yu, Zhiyong Mean-field type FBSDEs under domination-monotonicity conditions and application to LQ problems. (English) Zbl 1511.93145 SIAM J. Control Optim. 61, No. 1, 22-46 (2023). MSC: 93E20 60H10 49N10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liu, Ruyi; Wu, Zhen; Zhang, Detao Two equivalent families of linear fully coupled forward backward stochastic differential equations. (English) Zbl 1511.60088 ESAIM, Control Optim. Calc. Var. 28, Paper No. 82, 19 p. (2022). MSC: 60H10 34F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Hanxiao; Yong, Jiongmin; Zhou, Chao Backward stochastic differential equations and backward stochastic Volterra integral equations with anticipating generators. (English) Zbl 1502.60109 Probab. Uncertain. Quant. Risk 7, No. 4, 301-332 (2022). MSC: 60H20 60H10 93E20 60H07 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tian, Ran; Yu, Zhiyong Mean-field type FBSDEs in a domination-monotonicity framework and LQ multi-level Stackelberg games. (English) Zbl 1502.60097 Probab. Uncertain. Quant. Risk 7, No. 3, 215-246 (2022). MSC: 60H10 49N10 93E20 × Cite Format Result Cite Review PDF Full Text: DOI
Bensoussan, Alain; Cheung, Hang; Yam, Sheung Chi Phillip Control in Hilbert space and first-order mean field type problem. (English) Zbl 1502.93005 Yin, George (ed.) et al., Stochastic analysis, filtering, and stochastic optimization. A commemorative volume to honor Mark H. A. Davis’s contributions. Cham: Springer. 1-32 (2022). MSC: 93C25 49N80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gobet, Emmanuel; Grangereau, Maxime Newton method for stochastic control problems. (English) Zbl 1500.93145 SIAM J. Control Optim. 60, No. 5, 2996-3025 (2022). MSC: 93E20 49M15 60H30 49N10 × Cite Format Result Cite Review PDF Full Text: DOI
Sin, Myong-Guk; Ri, Kyong-Il; Kim, Kyong-Hui Existence and uniqueness of solution for coupled fractional mean-field forward-backward stochastic differential equations. (English) Zbl 1498.60272 Stat. Probab. Lett. 190, Article ID 109608, 11 p. (2022). MSC: 60H15 60G22 26A33 × Cite Format Result Cite Review PDF Full Text: DOI
Nam, Kihun; Xu, Yunxi Coupled FBSDEs with measurable coefficients and its application to parabolic PDEs. (English) Zbl 1491.60114 J. Math. Anal. Appl. 515, No. 1, Article ID 126403, 23 p. (2022). MSC: 60H30 35K10 93E20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ankirchner, Stefan; Fromm, Alexander; Wendt, Julian A transformation method to study the solvability of fully coupled FBSDEs. (English) Zbl 1496.60060 Stochastics 94, No. 1, 1-25 (2022). MSC: 60H10 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Yang, Xueyang; Yu, Zhiyong FBSDEs involving time delays and advancements on infinite horizon and LQ problems with delays. (English) Zbl 1485.93643 Syst. Control Lett. 161, Article ID 105149, 9 p. (2022). MSC: 93E20 49N10 93C15 60H30 × Cite Format Result Cite Review PDF Full Text: DOI
Fujii, Masaaki; Takahashi, Akihiko Equilibrium price formation with a major player and its mean field limit. (English) Zbl 1485.49047 ESAIM, Control Optim. Calc. Var. 28, Paper No. 21, 36 p. (2022). MSC: 49N80 91A16 91B50 91B70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Yu, Zhiyong On forward-backward stochastic differential equations in a domination-monotonicity framework. (English) Zbl 1492.60180 Appl. Math. Optim. 85, No. 1, 1-46 (2022). MSC: 60H10 49N10 93E20 × Cite Format Result Cite Review PDF Full Text: DOI
Zheng, Guoqiang Local wellposedness of coupled backward stochastic differential equations driven by \(G\)-Brownian motions. (English) Zbl 1481.60118 J. Math. Anal. Appl. 506, No. 1, Article ID 125540, 18 p. (2022). MSC: 60H10 60G65 × Cite Format Result Cite Review PDF Full Text: DOI
Zhu, Qingfeng; Shi, Yufeng; Teng, Bin Forward-backward doubly stochastic differential equations with random jumps and related games. (English) Zbl 07878863 Asian J. Control 23, No. 2, 962-978 (2021). MSC: 93-XX × Cite Format Result Cite Review PDF Full Text: DOI
Taguchi, Dai; Tsuchiya, Takahiro Newton-Kantorovitch method for decoupled forward-backward stochastic differential equations. (English) Zbl 1505.60066 Electron. J. Differ. Equ. 2021, Paper No. 98, 16 p. (2021). Reviewer: Isamu Dôku (Saitama) MSC: 60H35 65C30 41A25 60H10 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Li, Na; Xiong, Jie; Yu, Zhiyong Linear-quadratic generalized Stackelberg games with jump-diffusion processes and related forward-backward stochastic differential equations. (English) Zbl 1481.60112 Sci. China, Math. 64, No. 9, 2091-2116 (2021). MSC: 60H10 91A65 93E20 × Cite Format Result Cite Review PDF Full Text: DOI
Kerimkulov, B.; Šiška, D.; Szpruch, L. A modified MSA for stochastic control problems. (English) Zbl 1472.93198 Appl. Math. Optim. 84, No. 3, 3417-3436 (2021). MSC: 93E20 60H30 49M05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wei, Qingmeng; Yu, Zhiyong Infinite horizon forward-backward SDEs and open-loop optimal controls for stochastic linear-quadratic problems with random coefficients. (English) Zbl 1467.93340 SIAM J. Control Optim. 59, No. 4, 2594-2623 (2021). MSC: 93E20 60H10 49N10 × Cite Format Result Cite Review PDF Full Text: DOI
Zhu, Qing-feng; Zhang, Liang-quan; Shi, Yu-feng Infinite horizon forward-backward doubly stochastic differential equations and related SPDEs. (English) Zbl 1469.60201 Acta Math. Appl. Sin., Engl. Ser. 37, No. 2, 319-336 (2021). MSC: 60H10 60H15 × Cite Format Result Cite Review PDF Full Text: DOI
Hu, Ying; Li, Xun; Wen, Jiaqiang Anticipated backward stochastic differential equations with quadratic growth. (English) Zbl 1467.60041 J. Differ. Equations 270, 1298-1331 (2021). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60H10 60H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Yong, Jiongmin \(L^p\)-theory of forward-backward stochastic differential equations. (English) Zbl 1460.60059 Jakubowski, Jacek (ed.) et al., Stochastic modeling and control. Based on the Simons semester, Warsaw, Poland, January 2 – March 31, 2019. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 122, 255-286 (2020). MSC: 60H10 49N05 93E20 × Cite Format Result Cite Review PDF Full Text: DOI
Xu, Xiaoming Fully coupled forward-backward stochastic functional differential equations and applications to quadratic optimal control. (English) Zbl 1460.93111 J. Syst. Sci. Complex. 33, No. 6, 1886-1902 (2020). MSC: 93E20 93C23 34K50 49N10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Al-Hussein, AbdulRahman; Gherbal, Boulakhras Existence and uniqueness of the solutions of forward-backward doubly stochastic differential equations with Poisson jumps. (English) Zbl 1457.60085 Random Oper. Stoch. Equ. 28, No. 4, 253-268 (2020). MSC: 60H10 60G55 60H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ankirchner, Stefan; Fromm, Alexander; Kruse, Thomas; Popier, Alexandre Optimal position targeting via decoupling fields. (English) Zbl 1445.49001 Ann. Appl. Probab. 30, No. 2, 644-672 (2020). MSC: 49J05 60H99 60G99 93E20 49K15 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Shi, Yufeng; Zhao, Huaizhong Forward-backward stochastic differential equations on infinite horizon and quasilinear elliptic PDEs. (English) Zbl 1431.60049 J. Math. Anal. Appl. 485, No. 1, Article ID 123791, 19 p. (2020). MSC: 60H10 60H15 60H30 60J60 × Cite Format Result Cite Review PDF Full Text: DOI Link
Xie, Bing; Yu, Zhiyong An exploration of \(L^p\)-theory for forward-backward stochastic differential equations with random coefficients on small durations. (English) Zbl 1471.60092 J. Math. Anal. Appl. 483, No. 2, Article ID 123642, 18 p. (2020). MSC: 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Tianxiao; Yong, Jiongmin Backward stochastic Volterra integral equations – representation of adapted solutions. (English) Zbl 1427.60140 Stochastic Processes Appl. 129, No. 12, 4926-4964 (2019). MSC: 60H20 45D05 35K15 35K40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hu, Mingshang; Ji, Shaolin; Xue, Xiaole The existence and uniqueness of viscosity solution to a kind of Hamilton-Jacobi-Bellman equation. (English) Zbl 1472.93196 SIAM J. Control Optim. 57, No. 6, 3911-3938 (2019). Reviewer: Lu Qi (Chengdu) MSC: 93E20 60H10 49L25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liu, Ruyi; Wu, Zhen Well-posedness of fully coupled linear forward-backward stochastic differential equations. (English) Zbl 1414.93205 J. Syst. Sci. Complex. 32, No. 3, 789-802 (2019). MSC: 93E20 93C15 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Sun, Jingrui; Yong, Jiongmin Linear-quadratic stochastic two-person nonzero-sum differential games: open-loop and closed-loop Nash equilibria. (English) Zbl 1405.91025 Stochastic Processes Appl. 129, No. 2, 381-418 (2019). MSC: 91A15 91A23 91A05 60H10 49N70 49N10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Haiyang; Zhang, Jianfeng Forward backward SDEs in weak formulation. (English) Zbl 1419.60041 Math. Control Relat. Fields 8, No. 3-4, 1021-1049 (2018). MSC: 60H07 60H30 35R60 34F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Shuping Jiongmin Yong’s mathematical works in recent thirty years. (English) Zbl 1416.01022 Math. Control Relat. Fields 8, No. 3-4, 491-500 (2018). MSC: 01A70 93-03 × Cite Format Result Cite Review PDF Full Text: DOI
Xu, Juanjuan; Zhang, Huanshui; Xie, Lihua General linear forward and backward stochastic difference equations with applications. (English) Zbl 1406.93387 Automatica 96, 40-50 (2018). MSC: 93E20 39A50 93C23 93C05 49N10 × Cite Format Result Cite Review PDF Full Text: DOI
Liu, Ruyi; Wu, Zhen Well-posedness of a class of two-point boundary value problems associated with ordinary differential equations. (English) Zbl 1445.34049 Adv. Difference Equ. 2018, Paper No. 54, 12 p. (2018). MSC: 34B10 34C20 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Na; Yu, Zhiyong Forward-backward stochastic differential equations and linear-quadratic generalized Stackelberg games. (English) Zbl 1417.91150 SIAM J. Control Optim. 56, No. 6, 4148-4180 (2018). MSC: 91A65 93E20 60H10 49N10 × Cite Format Result Cite Review PDF Full Text: DOI
Feng, Chunrong; Wang, Xince; Zhao, Huaizhong Quasi-linear PDEs and forward-backward stochastic differential equations: weak solutions. (English) Zbl 1516.35184 J. Differ. Equations 264, No. 2, 959-1018 (2018). MSC: 35D30 35J62 35K59 × Cite Format Result Cite Review PDF Full Text: DOI
Guerdouh, Dalila; Khelfallah, Nabil Forward-backward SDEs driven by Lévy process in stopping time duration. (English) Zbl 1372.60121 Commun. Math. Stat. 5, No. 2, 141-157 (2017). MSC: 60J75 60H30 × Cite Format Result Cite Review PDF Full Text: DOI
Huang, Jianhui; Wang, Shujun; Wu, Zhen Backward-forward linear-quadratic mean-field games with major and minor agents. (English) Zbl 1443.91044 Probab. Uncertain. Quant. Risk 1, Paper No. 8, 27 p. (2016). MSC: 91A16 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Al-Hussein, Abdulrahman; Gherbal, Boulakhras Sufficient conditions of optimality for forward-backward doubly SDEs with jumps. (English) Zbl 1403.93193 Eddahbi, M’hamed (ed.) et al., Statistical methods and applications in insurance and finance. CIMPA school, Marrakech and Kelaat M’gouna, Morocco, April 8–20, 2013. Cham: Springer (ISBN 978-3-319-30416-8/hbk; 978-3-319-30417-5/ebook). Springer Proceedings in Mathematics & Statistics 158, 173-191 (2016). MSC: 93E20 49K45 60H10 60J75 × Cite Format Result Cite Review PDF Full Text: DOI
de Oliveira Gomes, André Asymptotics for FBSDES with jumps and connections with partial integral differential equations. (English) Zbl 1349.35388 Gonçalves, Patrícia (ed.) et al., From particle systems to partial differential equations III. Particle systems and PDEs III, Braga, Portugal, December 2014. Cham: Springer (ISBN 978-3-319-32142-4/hbk; 978-3-319-32144-8/ebook). Springer Proceedings in Mathematics & Statistics 162, 99-120 (2016). MSC: 35R09 × Cite Format Result Cite Review PDF Full Text: DOI
Yong, Jiongmin Forward-backward evolution equations and applications. (English) Zbl 06648252 Math. Control Relat. Fields 6, No. 4, 653-704 (2016). MSC: 47J35 47D06 35K90 35L90 49K27 34G20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Na; Yu, Zhiyong Recursive stochastic linear-quadratic optimal control and nonzero-sum differential game problems with random jumps. (English) Zbl 1422.60098 Adv. Difference Equ. 2015, Paper No. 144, 19 p. (2015). MSC: 60H10 93E20 91A15 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Liangquan; Huang, Jianhui; Li, Xun Necessary condition for near optimal control of linear forward-backward stochastic differential equations. (English) Zbl 1337.93102 Int. J. Control 88, No. 8, 1594-1608 (2015). MSC: 93E20 49K45 60H10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Tian Xiao; Shi, Yu Feng Linear quadratic stochastic integral games and related topics. (English) Zbl 1331.60125 Sci. China, Math. 58, No. 11, 2405-2420 (2015). MSC: 60H20 49N10 91A15 60H05 93E20 45D99 49K21 × Cite Format Result Cite Review PDF Full Text: DOI
Nie, TianYang Forward-backward stochastic differential equation with subdifferential operator and associated variational inequality. (English) Zbl 1322.60094 Sci. China, Math. 58, No. 4, 729-748 (2015). MSC: 60H10 60H30 49J40 49J52 × Cite Format Result Cite Review PDF Full Text: DOI
Nie, Tianyang A stochastic approach to a new type of parabolic variational inequalities. (English) Zbl 1341.60071 Stochastics 87, No. 3, 477-517 (2015). MSC: 60H30 60H10 49J40 35D40 49J55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ma, Jin; Wu, Zhen; Zhang, Detao; Zhang, Jianfeng On well-posedness of forward-backward SDEs – a unified approach. (English) Zbl 1319.60132 Ann. Appl. Probab. 25, No. 4, 2168-2214 (2015). MSC: 60H10 60H20 60H07 60G60 60H30 34F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Li, Juan; Wei, Qingmeng Stochastic differential games for fully coupled FBSDEs with jumps. (English) Zbl 1328.49037 Appl. Math. Optim. 71, No. 3, 411-448 (2015). MSC: 49N70 49J55 60H10 91A23 91A15 49L20 49L25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Delbaen, Freddy; Qiu, Jinniao; Tang, Shanjian Forward-backward stochastic differential systems associated to Navier-Stokes equations in the whole space. (English) Zbl 1323.35010 Stochastic Processes Appl. 125, No. 7, 2516-2561 (2015). Reviewer: Luisa Consiglieri (Lisboa) MSC: 35D35 35R60 35Q30 60H15 76D05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Guangchen; Xiao, Hua Arrow sufficient conditions for optimality of fully coupled forward-backward stochastic differential equations with applications to finance. (English) Zbl 1312.93106 J. Optim. Theory Appl. 165, No. 2, 639-656 (2015). MSC: 93E11 93E20 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Casserini, Matteo; Liang, Gechun Fully coupled forward-backward stochastic dynamics and functional differential systems. (English) Zbl 1314.60112 Stoch. Dyn. 15, No. 2, Article ID 1550006, 25 p. (2015). MSC: 60H10 60H30 34K50 93E03 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ji, Shaolin; Yang, Shuzhen Solutions for functional fully coupled forward-backward stochastic differential equations. (English) Zbl 1315.60068 Stat. Probab. Lett. 99, 70-76 (2015). MSC: 60H10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Ruijing; Liu, Bin A maximum principle for fully coupled stochastic control systems of mean-field type. (English) Zbl 1326.49040 J. Math. Anal. Appl. 415, No. 2, 902-930 (2014). MSC: 49K45 93E20 60H10 49N10 × Cite Format Result Cite Review PDF Full Text: DOI
Wu, Zhen; Yu, Zhiyong Probabilistic interpretation for a system of quasilinear parabolic partial differential equation combined with algebra equations. (English) Zbl 1314.60135 Stochastic Processes Appl. 124, No. 12, 3921-3947 (2014). MSC: 60H30 60H10 35K59 35C99 × Cite Format Result Cite Review PDF Full Text: DOI
Yin, Hong Solvability of forward-backward stochastic partial differential equations. (English) Zbl 1329.60224 Stochastic Processes Appl. 124, No. 8, 2583-2604 (2014). MSC: 60H15 35R60 × Cite Format Result Cite Review PDF Full Text: DOI
Horst, Ulrich; Hu, Ying; Imkeller, Peter; Réveillac, Anthony; Zhang, Jianing Forward-backward systems for expected utility maximization. (English) Zbl 1329.60182 Stochastic Processes Appl. 124, No. 5, 1813-1848 (2014). MSC: 60H10 93E20 91B16 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Yu, Zhiyong Linear - quadratic optimal control and nonzero-sum differential game of forward-backward stochastic system. (English) Zbl 1282.93280 Asian J. Control 14, No. 1, 173-185 (2012). MSC: 93E20 60H10 49N10 49N70 × Cite Format Result Cite Review PDF Full Text: DOI
Ji, Shaolin; Wei, Qingmeng; Zhang, Xiumin A maximum principle for controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal state constraints. (English) Zbl 1256.49007 Abstr. Appl. Anal. 2012, Article ID 537376, 29 p. (2012). MSC: 49J20 35R60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhu, QingFeng; Shi, YuFeng Forward-backward doubly stochastic differential equations and related stochastic partial differential equations. (English) Zbl 1305.60050 Sci. China, Math. 55, No. 12, 2517-2534 (2012). Reviewer: Henri Schurz (Carbondale) MSC: 60H10 60H15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Li; Wu, Zhen; Yu, Zhiyong Delayed stochastic linear-quadratic control problem and related applications. (English) Zbl 1251.93138 J. Appl. Math. 2012, Article ID 835319, 22 p. (2012). MSC: 93E20 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Jin; Yin, Hong; Zhang, Jianfeng On non-Markovian forward-backward SDEs and backward stochastic PDEs. (English) Zbl 1260.60123 Stochastic Processes Appl. 122, No. 12, 3980-4004 (2012). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 60H15 60H10 34F05 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Detao Backward linear-quadratic stochastic optimal control and nonzero-sum differential game problem with random jumps. (English) Zbl 1255.93154 J. Syst. Sci. Complex. 24, No. 4, 647-662 (2011). MSC: 93E20 49N10 49N70 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Jin; Zhang, Jianfeng On weak solutions of forward-backward SDEs. (English) Zbl 1235.60067 Probab. Theory Relat. Fields 151, No. 3-4, 475-507 (2011). MSC: 60H10 34F05 × Cite Format Result Cite Review PDF Full Text: DOI
Yin, Juliang Forward-backward SDEs with random terminal time and applications to pricing special European-type options for a large investor. (English) Zbl 1230.60064 Bull. Sci. Math. 135, No. 8, 883-895 (2011). MSC: 60H10 60H20 91B24 × Cite Format Result Cite Review PDF Full Text: DOI
Liang, Gechun; Lyons, Terry; Qian, Zhongmin Backward stochastic dynamics on a filtered probability space. (English) Zbl 1238.60064 Ann. Probab. 39, No. 4, 1422-1448 (2011). Reviewer: Nicolas Perkowski (Berlin) MSC: 60H10 60H30 60J45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Li; Wu, Zhen A type of general forward-backward stochastic differential equations and applications. (English) Zbl 1218.60047 Chin. Ann. Math., Ser. B 32, No. 2, 279-292 (2011). MSC: 60H10 93E20 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Jin; Yong, Jiongmin; Zhao, Yanhong Four step scheme for general Markovian forward-backward SDEs. (English) Zbl 1217.60056 J. Syst. Sci. Complex. 23, No. 3, 546-571 (2010). Reviewer: Andrew Dale (Durban) MSC: 60H15 60H10 34F05 35R60 × Cite Format Result Cite Review PDF Full Text: DOI
Shi, J. T.; Wu, Z. Maximum principle for partially-observed optimal control of fully-coupled forward-backward stochastic systems. (English) Zbl 1209.49034 J. Optim. Theory Appl. 145, No. 3, 543-578 (2010). MSC: 49K45 49N10 93E20 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Yong, Jiongmin Forward-backward stochastic differential equations with mixed initial-terminal conditions. (English) Zbl 1185.60067 Trans. Am. Math. Soc. 362, No. 2, 1047-1096 (2010). MSC: 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Zhu, Qing-feng; Shi, Yu-feng; Gong, Xian-jun Solutions to general forward-backward doubly stochastic differential equations. (English) Zbl 1166.60318 Appl. Math. Mech., Engl. Ed. 30, No. 4, 517-526 (2009). MSC: 60H10 60H20 × Cite Format Result Cite Review PDF Full Text: DOI
Yin, Juliang On solutions of a class of infinite horizon FBSDEs. (English) Zbl 1151.60031 Stat. Probab. Lett. 78, No. 15, 2412-2419 (2008). MSC: 60H10 60H20 × Cite Format Result Cite Review PDF Full Text: DOI
Bahlali, Seid; Labed, Boubakeur Necessary and sufficient conditions of optimality for optimal control problem with initial and terminal costs. (English) Zbl 1113.93105 Random Oper. Stoch. Equ. 14, No. 3, 291-301 (2006). Reviewer: Mikhail P. Moklyachuk (Kyïv) MSC: 93E20 60H10 62P05 × Cite Format Result Cite Review PDF Full Text: DOI
Delarue, F.; Guatteri, G. Weak existence and uniqueness for forward-backward SDEs. (English) Zbl 1113.60059 Stochastic Processes Appl. 116, No. 12, 1712-1742 (2006). Reviewer: Melvin D. Lax (Long Beach) MSC: 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Yong, Jiongmin Linear forward-backward stochastic differential equations with random coefficients. (English) Zbl 1120.60058 Probab. Theory Relat. Fields 135, No. 1, 53-83 (2006). MSC: 60H10 93C05 93E99 × Cite Format Result Cite Review PDF Full Text: DOI
Wu, Zhen; Yu, Zhi-Yong Linear quadratic nonzero-sum differential games with random jumps. (English) Zbl 1144.91305 Appl. Math. Mech., Engl. Ed. 26, No. 8, 1034-1039 (2005). MSC: 91A23 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Wu, Zhen Fully coupled FBSDE with Brownian motion and Poisson process in stopping time duration. (English) Zbl 1029.60047 J. Aust. Math. Soc. 74, No. 2, 249-266 (2003). Reviewer: Yuliya S.Mishura (Kyïv) MSC: 60H10 60G40 × Cite Format Result Cite Review PDF Full Text: DOI
Peng, Shige; Shi, Yufeng A type of time-symmetric forward-backward stochastic differential equations. (English. Abridged French version) Zbl 1031.60055 C. R., Math., Acad. Sci. Paris 336, No. 9, 773-778 (2003). MSC: 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Antonelli, Fabio; Ma, Jin Weak solutions of forward-backward SDE’s. (English) Zbl 1055.60055 Stochastic Anal. Appl. 21, No. 3, 493-514 (2003). Reviewer: Rainer Buckdahn (Brest) MSC: 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Delarue, François On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case. (English) Zbl 1058.60042 Stochastic Processes Appl. 99, No. 2, 209-286 (2002). MSC: 60H10 × Cite Format Result Cite Review PDF Full Text: DOI