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Backward stochastic differential equations with rank-based data

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Abstract

In this paper, we investigate Markovian backward stochastic differential equations (BSDEs) with the generator and the terminal value that depend on the solutions of stochastic differential equations with rankbased drift coefficients. We study regularity properties of the solutions of this kind of BSDEs and establish their connection with semi-linear backward parabolic partial differential equations in simplex with Neumann boundary condition. As an application, we study the European option pricing problem with capital size based stock prices.

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Acknowledgements

This work was supported by National Science Foundation of USA (Grant No. DMS-1206276) and National Natural Science Foundation of China (Grant No.11601280). The authors thank Professors Shige Peng, Zengjing Chen and Andrey Sarantsev for helpful discussions. The authors also thank the referees for helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Zhen-qing Chen

  2. School of Mathematics, Shandong University, Jinan, 250100, China

    Xinwei Feng

  3. Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China

    Xinwei Feng

Authors
  1. Zhen-qing Chen
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  2. Xinwei Feng
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Correspondence to Xinwei Feng.

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Chen, Zq., Feng, X. Backward stochastic differential equations with rank-based data. Sci. China Math. 61, 27–56 (2018). https://doi.org/10.1007/s11425-017-9125-6

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  • DOI: https://doi.org/10.1007/s11425-017-9125-6

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