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Representation Theorem for Generators of Quadratic BSDEs

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Abstract

In this paper, we establish a general representation theorem for generator of backward stochastic differential equation (BSDE), whose generator has a quadratic growth in z. As some applications, we obtain a general converse comparison theorem of such quadratic BSDEs and uniqueness theorem, translation invariance for quadratic g-expectation.

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Acknowledgements

The authors would like to thank the anonymous referee for their valuable comments and suggestions.

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Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, China

    Shi-qiu Zheng & Shou-mei Li

  2. College of Sciences, North China University of Science and Technology, Tangshan, 063210, China

    Shi-qiu Zheng

Authors
  1. Shi-qiu Zheng
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  2. Shou-mei Li
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Corresponding author

Correspondence to Shou-mei Li.

Additional information

The authors are supported by the National Natural Science Foundation of China (No. 11571024) and Natural Science Foundation of Beijing (No. 1132008). The first author is also supported by a program of Hebei province (No. QN2017116).

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Zheng, Sq., Li, Sm. Representation Theorem for Generators of Quadratic BSDEs. Acta Math. Appl. Sin. Engl. Ser. 34, 622–635 (2018). https://doi.org/10.1007/s10255-018-0772-8

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  • DOI: https://doi.org/10.1007/s10255-018-0772-8

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