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Survey on Path-Dependent PDEs

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Abstract

In this paper, the authors provide a brief introduction of the path-dependent partial di.erential equations (PDEs for short) in the space of continuous paths, where the path derivatives are in the Dupire (rather than Fréchet) sense. They present the connections between Wiener expectation, backward stochastic di.erential equations (BSDEs for short) and path-dependent PDEs. They also consider the well-posedness of path-dependent PDEs, including classical solutions, Sobolev solutions and viscosity solutions.

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Author information

Authors and Affiliations

  1. School of Mathematics, Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, 250100, China

    Shige Peng

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yongsheng Song

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yongsheng Song

  4. Zhongtai Securities Institute for Financial Studies, School of Mathematics, Shandong University, Jinan, 250100, China

    Falei Wang

Authors
  1. Shige Peng
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  2. Yongsheng Song
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  3. Falei Wang
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Corresponding authors

Correspondence to Shige Peng, Yongsheng Song or Falei Wang.

Ethics declarations

Conflicts of interest Shige PENG is an editorial board member for Chinese Annals of Mathematics Series B and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no conflicts of interest.

Additional information

This work was supported by the National Key R&D Program of China (Nos. 2018YFA0703900, 2020Y-FA0712700, 2018YFA0703901), the National Natural Science Foundation of China (Nos. 12031009, 12171280) and the Natural Science Foundation of Shandong Province (Nos. ZR2021YQ01, ZR2022JQ01).

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Peng, S., Song, Y. & Wang, F. Survey on Path-Dependent PDEs. Chin. Ann. Math. Ser. B 44, 837–856 (2023). https://doi.org/10.1007/s11401-023-0048-3

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  • DOI: https://doi.org/10.1007/s11401-023-0048-3

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