Adapted solution of a backward stochastic differential equation
Systems & Control Letters
A general stochastic maximum principle for optimal control problems
SIAM Journal on Control and Optimization
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Numerical Algorithms for Forward-Backward Stochastic Differential Equations
SIAM Journal on Scientific Computing
A New Kind of Accurate Numerical Method for Backward Stochastic Differential Equations
SIAM Journal on Scientific Computing
On Numerical Approximations of Forward-Backward Stochastic Differential Equations
SIAM Journal on Numerical Analysis
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In this paper we propose a stable multistep scheme on time-space grids for solving backward stochastic differential equations. In our scheme, the integrands, which are conditional mathematical expectations derived from the original equations, are approximated by using Lagrange interpolating polynomials with values of the integrands at multiple time levels. They are then numerically evaluated using the Gauss-Hermite quadrature rules and polynomial interpolations on the spatial grids. Error estimates are rigorously proved for the semidiscrete version of the proposed scheme for backward stochastic differential equations with certain types of simplified generator functions. Finally, various numerical examples and comparisons with some other methods are presented to demonstrate high accuracy of the proposed multistep scheme.