Comparison Theorems of Backward Doubly Stochastic Differential Equations and Applications

Abstract A class of backward doubly stochastic differential equations (BDSDEs for short) are studied. We obtain a comparison theorem of these BDSDEs. As one of its applications, we derive the existence of solutions for BDSDEs with continuous coefficients.

[1]  S. Peng,et al.  Filtration-consistent nonlinear expectations and related g-expectations , 2002 .

[2]  S. Peng,et al.  Backward stochastic differential equations and quasilinear parabolic partial differential equations , 1992 .

[3]  S. Peng,et al.  Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control , 1999 .

[4]  Shige Peng,et al.  Duplicating and Pricing Contingent Claims in Incomplete Markets , 1999 .

[5]  David Nualart,et al.  Stochastic calculus with anticipating integrands , 1988 .

[6]  Larry G. Epstein,et al.  Stochastic differential utility , 1992 .

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

[8]  N. Karoui,et al.  Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market , 1995 .

[9]  S. Peng.  Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type , 1999 .

[10]  Shige Peng,et al.  Backward doubly stochastic differential equations and systems of quasilinear SPDEs , 1994 .

[11]  Larry G. Epstein,et al.  Ambiguity, risk, and asset returns in continuous time , 2000 .

[12]  S. Peng.  A Generalized dynamic programming principle and hamilton-jacobi-bellman equation , 1992 .

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

[14]  S. Peng,et al.  Reflected solutions of backward SDE's, and related obstacle problems for PDE's , 1997 .

[15]  Un schéma multipas d'approximation de l'équation de Langevin , 1991 .

[16]  Shige Peng,et al.  Probabilistic interpretation for systems of quasilinear parabolic partial differential equations , 1991 .

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

[18]  J. Lepeltier,et al.  Zero-sum stochastic differential games and backward equations , 1995 .

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

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

[21]  M. Kobylanski,et al.  Résultats d'existence et d'unicité pour des équations différentielles stochastiques rétrogrades avec des générateurs à croissance quadratique , 1997 .