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). Summary: We study a type of time-symmetric forward-backward stochastic differential equations. Under some monotonicity assumptions, we establish the existence and uniqueness theorem by means of a method of continuation. We also give an application. Cited in 1 ReviewCited in 38 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:forward-backward stochastic differential equations; method of continuation × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Antonelli, F., Backward-forward stochastic differential equations, Ann. Appl. Probab., 3, 777-793 (1993) · Zbl 0780.60058 [2] Bensoussan, A., Stochastic Control by Functional Analysis Methods (1982), North-Holland: North-Holland Amsterdam · Zbl 0474.93002 [3] Bismut, J.-M., Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl., 44, 384-404 (1973) · Zbl 0276.93060 [4] El Karoui, N.; Peng, S.; Quenez, M.-C., Backward stochastic differential equations in finance, Math. Finance, 7, 1-71 (1997) · Zbl 0884.90035 [5] Hu, Y.; Peng, S., Solution of forward-backward stochastic differential equations, Probab. Theory Related Fields, 103, 273-283 (1995) · Zbl 0831.60065 [6] Ma, J.; Protter, P.; Yong, J., Solving forward-backward stochastic differential equations explicitly – a four step scheme, Probab. Theory Related Fields, 98, 339-359 (1994) · Zbl 0794.60056 [7] Pardoux, E.; Peng, S., Adapted solution of a backward stochastic differential equation, Systems Control Lett., 14, 55-61 (1990) · Zbl 0692.93064 [8] Pardoux, E.; Peng, S., Backward doubly stochastic differential equations and systems of quasilinear parabolic SPDE’s, Probab. Theory Related Fields, 98, 209-227 (1994) · Zbl 0792.60050 [9] Peng, S., Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics, 37, 61-74 (1991) · Zbl 0739.60060 [10] Peng, S., Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions, Stochastic Process. Appl., 88, 259-290 (2000) · Zbl 1045.60061 [11] Peng, S.; Shi, Y., Infinite horizon forward-backward stochastic differential equations, Stochastic Process. Appl., 85, 75-92 (2000) · Zbl 0997.60062 [12] Peng, S.; Wu, Z., Fully coupled forward-backward stochastic differential equations and applications to optimal control, SIAM J. Control Optim., 37, 825-843 (1999) · Zbl 0931.60048 [13] Yong, J., Finding adapted solutions of forward-backward stochastic differential equations – method of continuation, Probab. Theory Related Fields, 107, 537-572 (1997) · Zbl 0883.60053 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.