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An Explicit Second-Order Numerical Scheme to Solve Decoupled Forward Backward Stochastic Equations

  • Yu Fu (a1) and Weidong Zhao (a1)

Abstract

An explicit numerical scheme is proposed for solving decoupled forward backward stochastic differential equations (FBSDE) represented in integral equation form. A general error inequality is derived for this numerical scheme, which also implies its stability. Error estimates are given based on this inequality, showing that the explicit scheme can be second-order. Some numerical experiments are carried out to illustrate the high accuracy of the proposed scheme.

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Corresponding author

Corresponding author. Email address: nielf0614@126.com
* Corresponding author. Email address: wdzhao@sdu.edu.cn

References

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[1] Bender, C. and Denk, R., A forward scheme for backward sdes, Stoch. Proc. Appl. 117, 17931812 (2007).
[2] Delarue, F., On the existence and uniqueness of solutions to fbsdes in a non-degenerate case, Stoch. Proc. Appl. 99, 209286 (2002.
[3] Douglas, J., Ma, J. and Protter, P., Numerical methods for forward-backward stochastic differential equations, Ann. Appl. Probab. 6, 940968 (1996).
[4] Gobet, E. and Labart, C., Error expansion for the discretization of backward stochastic differential equations, Stoch. Proc. Appl. 117, 803829 (2007).
[5] Karou, N. NL., Peng, S., and Quenez, M. C., Backward stochastic differential equations in finance, Math. Finance 7, 171 (1997).
[6] Kloeden, P. E. and Platen, E., Numerical Solutions of Stochastic Differential Equations, Springer, Berlin and Heidelberg (1992).
[7] Ma, J., Protter, P., Martin, J. S., and Torres, S., Numerical method for backward stochastic differential equations, Ann. Appl. Probab. 12, 302316 (2002).
[8] Ma, J., Protter, P., and Yong, J., Solving forward-backward stochastic differential equations explicitly - a four step scheme, Probab. Theory Related Fields 98, 339359 (1994).
[9] Ma, J., Shen, J., and Zhao, Y., On numerical approximations of forward-backward stochastic differential equations, SIAM J. Numer. Anal. 46, 26362661 (2008).
[10] Ma, J. and Yong, J., Forward-Backward Stochastic Differential Equations and their Applications, Springer, Berlin (1999).
[11] Milstein, G. N. and Tretyakov, M. V., Numerical algorithms for forward-backward stochastic differential equations, SIAM J. Sci. Comput. 28, 561582 (2006).
[12] Oksendal, B., Stochastic Differential Equations: An Introduction with Applications, Springer, Berlin (2003).
[13] Pardoux, E. and Peng, S., Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14, 5661 (1990).
[14] Peng, S., Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics and Stochastic Reports 37, 6174 (1991).
[15] Zhao, W., Chen, L., and Peng, S., A new kind of accurate numerical method for backward stochastic differential equations, SIAM J. Sci. Comput. 28, 15631581 (2006).
[16] Zhao, W., Fu, Y., and Zhou, T., New kinds of high-order multistep schemes for coupled forward backward stochastic differential equations, SIAM J. Sci. Comput. 36, A1731A1751 (2014).
[17] Zhao, W., Zhang, G., and Ju, L., A stable multistep schemes for backward stochastic differential equations, SIAM J. Numer. Anal. 48, 13691394 (2010).
[18] Zhao, W., Zhang, W., and Ju, L., A numerical method and its error estimates for the decoupled forward-backward stochastic differential equations, Comm. Comput. Phys. 15, 618646 (2014).

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An Explicit Second-Order Numerical Scheme to Solve Decoupled Forward Backward Stochastic Equations

  • Yu Fu (a1) and Weidong Zhao (a1)

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