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Strong Stability Preserving Multistep Schemes for Forward Backward Stochastic Differential Equations

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Abstract

In this work, we are concerned with strong stability preserving multistep (SSPM) schemes for forward backward stochastic differential equations (FBSDEs). To this aim, we first perform a comprehensive analysis on a general type of multistep schemes for FBSDEs, based on which we present new sufficient conditions on the coefficients such that the associated schemes are stable and enjoy certain order of consistency. Upon these results, we propose a practical way to design high-order SSPM schemes for FBSDEs. Numerical experiments are carried out to demonstrate the strong stability of our SSPM schemes.

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Funding

The work of the authors was partially supported by the National Natural Science Foundation of China Grants (Grant Nos. 12071261, 11822111, 11831010, 11688101, 11871068), and the National Key R &D Programs Grants (Grant Nos. 2020YFA0712000, 2018YFA0703900).

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Authors and Affiliations

  1. School of Mathematics, Institute of Finance, Shandong University, Jinan, 250100, Shandong, People’s Republic of China

    Shuixin Fang & Weidong Zhao

  2. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Tao Zhou

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  1. Shuixin Fang
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Correspondence to Weidong Zhao.

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The work of the authors was partially supported by the National Natural Science Foundation of China Grants (Grant Nos. 12071261, 11822111, 11831010, 11688101, 11871068), and the National Key R &D Programs Grants (Grant Nos. 2020YFA0712000, 2018YFA0703900).

A Additional Optimal SSPM Schemes

A Additional Optimal SSPM Schemes

In Table 7, we present coefficients for optimal SSPM schemes with order upto 5.

Table 7 SSPM schemes under uniform time partitions (Part 2)
Full size table

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Fang, S., Zhao, W. & Zhou, T. Strong Stability Preserving Multistep Schemes for Forward Backward Stochastic Differential Equations. J Sci Comput 94, 53 (2023). https://doi.org/10.1007/s10915-023-02111-x

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