Second-order schemes for solving decoupled forward backward stochastic differential equations

被引：0
作者：
WeiDong Zhao
Yang Li
Yu Fu
机构：
[1] Shandong University,School of Mathematics
[2] University of Shanghai for Science and Technology,College of Science
来源：
Science China Mathematics | 2014年 / 57卷
关键词：
forward backward stochastic differential equations; second-order scheme; error estimate; trapezoidal rule; Malliavin calculus; 65C20; 60H35;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, by using trapezoidal rule and the integration-by-parts formula of Malliavin calculus, we propose three new numerical schemes for solving decoupled forward-backward stochastic differential equations. We theoretically prove that the schemes have second-order convergence rate. To demonstrate the effectiveness and the second-order convergence rate, numerical tests are given.
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页码：665 / 686
页数：21
相关论文
共 38 条
[1]  
Bender C(2007)A forward scheme for backward SDEs Stochastic Process Appl 117 1793-1812
[2]  
Denk R(2004)Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations Stochastic Process Appl 111 175-206
[3]  
Bouchard B(2007)Error expansion for the discretization of backward stochastic differential equations Stochastic Process Appl 117 803-829
[4]  
Touzi N(1997)Backward stochastic differential equations in finance Math Finance 7 1-71
[5]  
Gobet E(2010)-error estimates for numerical schemes for solving certain kinds of backward stochastic differential equations Statist Probab Lett 21–22 1612-1617
[6]  
Labart C(2002)Numerical methods for backward stochastic differential equations Ann Appl Probab 12 302-316
[7]  
Karoui N E(1994)Solving forward-backward stochastic differential equations explicitly-a four step scheme Probab Theory Related Fields 98 339-359
[8]  
Peng S G(1990)Adapted solution of a backward stochastic differntial equation Systems Control Lett 14 55-61
[9]  
Quenez M C(1991)Probabilistic interpretation for systems of quasilinear parabolic partial differential equations Stoch Rep 37 61-74
[10]  
Li Y(2003)Weak second order conditions for stochastic Runge-Kutta methods SIAM J Sci Comput 2 507-523
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