Mean-field backward stochastic differential equations driven by G-Brownian motion and related partial differential equations |
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Authors: | Shengqiu Sun |
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Affiliation: | School of Mathematics, Shandong University, Jinan, China |
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Abstract: | In this paper, we study mean-field backward stochastic differential equations driven by G-Brownian motion (G-BSDEs). We first obtain the existence and uniqueness theorem of these equations. In fact, we can obtain local solutions by constructing Picard contraction mapping for Y term on small interval, and the global solution can be obtained through backward iteration of local solutions. Then, a comparison theorem for this type of mean-field G-BSDE is derived. Furthermore, we establish the connection of this mean-field G-BSDE and a nonlocal partial differential equation. Finally, we give an application of mean-field G-BSDE in stochastic differential utility model. |
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Keywords: | comparison theorem Feynman-Kac formula special t4ht@.G-Brownian motion mean-field backward stochastic differential equations |
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