Numerical Computations for Backward Doubly SDEs and SPDEs
نویسندگان
چکیده
Since Pardoux and Peng introduced backward stochastic differential equations (BSDEs in short), the theory of BSDEs has been widely developed, mainly because of a large part of problems in mathematical finance can be treated as a BSDE. However it is known that only a limited number of BSDE can be solved explicitly. To develop numerical method and numerical algorithm is very helpful, theoretically and practically. Recently many different types of discretization of BDSDE and the related numerical analysis were introduced. On the other hand, Paroux and Peng [8] introduced a new class of backward stochastic differential equations-backward ”doubly” stochastic differential equations and also showed the existence and uniqueness of the solution of BDSDE. But until now little work is devoted to the numerical method and the related numerical analysis. Here following the approach of Mémin, Peng and Xu [5], we present two numerical schemes of approximating solutions of BDSDE, and
منابع مشابه
Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions
Backward stochastic differential equations (BSDEs) were introduced by Pardoux and Peng [6], and it was shown in various papers that stochastic differential equations (SDEs) of this type give a probabilistic representation for the solution (at least in the viscosity sense) of a large class of system of semi-linear parabolic partial differential equations (PDEs). A new class of BSDEs, called back...
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