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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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
Keywords
- backward stochastic differential equations
- ranked particles
- named particles
- reflected Brownian motion
- partial differential equations
- viscosity solution