Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient

Abstract We prove existence, uniqueness and stability of the solution for multidimensional backward stochastic differential equations (BSDE) with locally monotone coefficient. This is done with an almost quadratic growth coefficient and a square integrable terminal data. The coefficient could be neither locally Lipschitz in the variable y nor in the variable z . To cite this article: K. Bahlali et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 757–762.

[1]  R. Carmona,et al.  BSDEs with polynomial growth generators , 2000 .

[2]  R. Darling,et al.  BACKWARDS SDE WITH RANDOM TERMINAL TIME AND APPLICATIONS TO SEMILINEAR ELLIPTIC PDE , 1997 .

[3]  M. Kobylanski.  Backward stochastic differential equations and partial differential equations with quadratic growth , 2000 .

[4]  K. Bahlali.  Existence and uniqueness of solutions for BSDEs with locally Lipschitz coefficient , 2002 .

[5]  Bahlali Khaled,et al.  Some generic properties in backward stochastic differential equations with continuous coefficient , 2001 .

[6]  On a general result for backward stochastic differential equations , 2002 .

[7]  Situ Rong.  On solutions of backward stochastic differential equations with jumps and applications , 1997 .

[8]  S. Peng,et al.  Backward Stochastic Differential Equations in Finance , 1997 .

[9]  Etienne Pardoux.  Backward stochastic di erential equations with subdi erential operator and related variational inequalities , 1998 .

[10]  S. Peng,et al.  Adapted solution of a backward stochastic differential equation , 1990 .

[11]  J. Lepeltier,et al.  Backward stochastic differential equations with continuous coefficient , 1997 .

[12]  X. Mao,et al.  Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients , 1995 .

[13]  Backward stochastic differential equation with local time , 1999 .

[14]  S. Hamadène.  Équations différentielles stochastiques rétrogrades : le cas localement lipschitzien , 1996 .

[15]  K. Bahlali.  Backward stochastic differential equations with locally Lipschitz coefficient , 2001 .

[16]  Jean-Pierre Lepeltier,et al.  Existence for BSDE with superlinear–quadratic coefficient , 1998 .

[17]  Infinite dimensional BSDE with jumps , 2002 .

[18]  F. Clarke,et al.  Nonlinear Analysis, Differential Equations and Control , 1999 .

[19]  É. Pardoux.  BSDEs, weak convergence and homogenization of semilinear PDEs , 1999 .

[20]  Multivalued backward stochastic differential equations with local lipschitz drift , 1997 .