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Infinite Horizon Forward-Backward Doubly Stochastic Differential Equations and Related SPDEs

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Abstract

A type of infinite horizon forward-backward doubly stochastic differential equations is studied. Under some monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of homotopy method. A probabilistic interpretation for solutions to a class of stochastic partial differential equations combined with algebra equations is given. A significant feature of this result is that the forward component of the FBDSDEs is coupled with the backward variable.

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Acknowledgments

The authors would like to thank the editors and the reviewers for their constructive comments and suggestions which helped us to improve this paper.

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Authors and Affiliations

  1. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, and Shandong Key Laboratory of Blockchain Finance, Jinan, 250014, China

    Qing-feng Zhu

  2. Institute for Financial Studies and School of Mathematics, Shandong University, Jinan, China

    Qing-feng Zhu & Yu-feng Shi

  3. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Liang-quan Zhang

Authors
  1. Qing-feng Zhu
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  2. Liang-quan Zhang
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  3. Yu-feng Shi
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Correspondence to Yu-feng Shi.

Additional information

This paper is supported by the National Natural Science Foundation of China (Nos. 11871309, 11671229, 11701040, 61871058, 11871010), Fundamental Research Funds for the Central Universities (2019XD-A11), National Key R&D Program of China (2018YFA0703900), Natural Science Foundation of Shandong Province (Nos. ZR2020MA032, ZR2019MA013), Special Funds of Taishan Scholar Project (tsqn20161041), and by the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions.

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Zhu, Qf., Zhang, Lq. & Shi, Yf. Infinite Horizon Forward-Backward Doubly Stochastic Differential Equations and Related SPDEs. Acta Math. Appl. Sin. Engl. Ser. 37, 319–336 (2021). https://doi.org/10.1007/s10255-021-1009-9

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  • DOI: https://doi.org/10.1007/s10255-021-1009-9

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