Abstract
A new numerical scheme of the Crank-Nicolson type for backward stochastic differential equations (BSDEs) is proposed. The Gauss-Hermite quadrature formula is used to approximate conditional mathematical expectations in the numerical applications, and space interpolations are used to compute values at non-space-grid points. Some numerical tests are given to validate the theoretical results.
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Supported in part by the China National Science Foundation under Grant No. 10671111 and China Project 973 under Grant No. 2007CB814906.
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Wang, Jl., Luo, Cx. & Zhao, WD. Crank-Nicolson scheme and its error estimates for backward stochastic differential equations. Acta Math. Appl. Sin. Engl. Ser. 1 (2009). https://doi.org/10.1007/s10255-009-9051-z
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DOI: https://doi.org/10.1007/s10255-009-9051-z
Keywords
- backward stochastic differential equations
- Crank-Nicolson scheme
- Gauss-Hermite quadrature formula
- time-space discretization