Backward stochastic differential equations with continuous coefficient. (English) Zbl 0904.60042

Summary: We prove the existence of a solution for “one-dimensional” backward stochastic differential equations where the coefficient is continuous, it has a linear growth, and the terminal condition is squared integrable. We also obtain the existence of a minimal solution.


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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[1] Barlow, M.; Perkins, E., One dimensional stochastic differential equations involving a singular increasing process, Stochastic, 12, 229-249 (1984) · Zbl 0543.60065
[2] Darling, R.; Pardoux, E., Backward SDE with random terminal time and applications to semilinear elliptic PDE, (Prépublication 96-02 du CMI (1995), Université de Provence) · Zbl 0895.60067
[3] El Karoui, N.; Peng, S.; Quenez, M. C., Backward stochastic differential equations in Finance, (Preprint Lab. de Probabilités de Paris VI (1994)) · Zbl 0884.90035
[4] Hamadene, S., Equations différentielles stochastiques rétrogrades: le cas localement lipschitzien, (to appear in: Ann. IHP (1994)) · Zbl 0893.60031
[5] Pardoux, E.; Peng, S., Adapted solution of a backward stochastic differential equation, Systems Control Lett., 14, 55-61 (1990) · Zbl 0692.93064
[6] Pardoux, E.; Peng, S., Some backward stochastic differential equations with non-lipschitz coefficients (1994), preprint
[7] Peng, S., A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equations, Stochastic, 38, 119-134 (1992) · Zbl 0756.49015
[8] Peng, S., \(L^2\) weak-convergence method and applications (1995), preprint
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