A New Kind of Accurate Numerical Method for Backward Stochastic Differential Equations

2006-01-01articleSIAM Journal on Scientific Computing151 citationsclosed

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Stochastic processes and financial applications Numerical methods for differential equations Fuzzy Systems and Optimization

Abstract

In this paper, we propose a new kind of numerical simulation method for backward stochastic differential equations (BSDEs). We discretize the continuous BSDEs on time‐space discrete grids, use the Monte Carlo method to approximate mathematical expectations, and use space interpolations to compute values at non‐grid points. To demonstrate the accuracy and the effectiveness of our method, several numerical examples are given.

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References

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2014Linear Multistep Schemes for BSDEs

2009Error estimates of the $\theta$-scheme for backward stochastic differentialequations

2018A kind of LQ non-zero sum differential game of backward stochastic differential equation with asymmetric information

2012A generalized $\theta$-scheme for solving backward stochastic differential equations

2013A Numerical Method and Its Error Estimates for the Decoupled Forward-Backward Stochastic Differential Equations