Abstract
In this paper, we present some assumptions to get the numerical scheme for backward doubly stochastic dierential delay equations (shortly-BDSDDEs), and we propose a scheme of BDSDDEs and discuss the numerical convergence and rate of convergence of our scheme.
Highlights
Backward stochastic differential equations have been first presented in Pardoux and Peng [16, 17] in order to proved existence and uniqueness of the adapted solutions and presented a new class of backward doubly stochastic differential equations, further investigations being
Delong [5, 6] studied applications of a new class of time-delayed BSDEs and he gives examples of pricing, hedging and portfolio management problems which could be established in the framework of backward stochastic differential delay equation
Using the Euler-Maruyama method, Xiaotai Wu and Litan Yan [20] defined the numerical solutions of doubly perturbed stochastic delay differential equations driven by Levy process, and they proved the numerical solutions converge to the exact solutions with the local Lipschitz condition
Summary
Backward stochastic differential equations ( shortly-BSDEs) have been first presented in Pardoux and Peng [16, 17] in order to proved existence and uniqueness of the adapted solutions and presented a new class of backward doubly stochastic differential equations, further investigations being (see [3, 4, 11, 13]). Wen Lu et al [19] investigated a class of multivalued backward doubly stochastic differential delay equation, and they proved the existence and uniqueness of the solutions for these equations under Lipschitz condition. Lu and Ren [12] established the existence and uniqueness of the solutions for a class of backward doubly stochastic differential equations with time delayed coefficients under Lipschitz condition. The purpose of this work is to study the numerical convergent of backward doubly stochastic delay differential equations We extend the approach of BDSDDEs in the general case, and introduce some general assumptions on the numerical convergence of backward doubly stochastic differential equations with time delayed coefficients.
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