Abstract
In this paper, we study the reflected solutions of one-dimensional backward stochastic differential equations driven by G-Brownian motion. The reflection keeps the solution above a given stochastic process. In order to derive the uniqueness of reflected G-BSDEs, we apply a “martingale condition” instead of the Skorohod condition. Similar to the classical case, we prove the existence by approximation via penalization. We then give some applications including a generalized Feynman-Kac formula of an obstacle problem for fully nonlinear partial differential equation and option pricing of American types under volatility uncertainty.
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Acknowledgements
This work was supported by the Tian Yuan Projection of the National Natural Science Foundation of China (Grant Nos. 11526205 and 11626247), the German Research Foundation (DFG) via CRC 1283 and the Lebesgue Center of Mathematics (“Investissements d’aveni” Program) (Grant No. ANR-11-LABX-0020-01). The authors thank Yongsheng Song and Falei Wang for their help and many useful discussions. The authors are grateful to the anonymous referees for their careful reading of the manuscript and many helpful suggestions.
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Li, H., Peng, S. & Soumana Hima, A. Reflected solutions of backward stochastic differential equations driven by G-Brownian motion. Sci. China Math. 61, 1–26 (2018). https://doi.org/10.1007/s11425-017-9176-0
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DOI: https://doi.org/10.1007/s11425-017-9176-0
Keywords
- G-expectation
- reflected backward stochastic differential equations
- obstacle problems for fully nonlinear PDEs