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An explicit second-order numerical scheme for mean-field forward backward stochastic differential equations

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Abstract

In this paper, we propose an explicit second-order scheme for solving decoupled mean-field forward backward stochastic differential equations. Its stability is theoretically proved, and its error estimates are rigorously deduced, which show that the proposed scheme is of second-order accurate when the weak-order 2.0 Itô-Taylor scheme is used to solve mean-field stochastic differential equations. Some numerical experiments are presented to verify the theoretical results.

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Acknowledgments

The authors would like to thank the referees for their valuable comments and suggestions which helped to improve much of the quality of the paper.

Funding

This research is partially supported by the science challenge Project (No. TZ2018001), the NSF of China (under Grant Nos. 11571351, 11571206, 11831010, 11871068)

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, Shandong, China

    Yabing Sun & Weidong Zhao

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  1. Yabing Sun
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  2. Weidong Zhao
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Correspondence to Weidong Zhao.

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Sun, Y., Zhao, W. An explicit second-order numerical scheme for mean-field forward backward stochastic differential equations. Numer Algor 84, 253–283 (2020). https://doi.org/10.1007/s11075-019-00754-2

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  • DOI: https://doi.org/10.1007/s11075-019-00754-2

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