Reflected mean-field backward stochastic differential equations. Approximation and associated nonlinear PDEs |
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Authors: | Juan Li |
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Institution: | School of Mathematics and Statistics, Shandong University (Weihai), Weihai 264209, PR China |
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Abstract: | Mathematical mean-field approaches have been used in many fields, not only in Physics and Chemistry, but also recently in Finance, Economics, and Game Theory. In this paper we will study a new special mean-field problem in a purely probabilistic method, to characterize its limit which is the solution of mean-field backward stochastic differential equations (BSDEs) with reflections. On the other hand, we will prove that this type of reflected mean-field BSDEs can also be obtained as the limit equation of the mean-field BSDEs by penalization method. Finally, we give the probabilistic interpretation of the nonlinear and nonlocal partial differential equations with the obstacles by the solutions of reflected mean-field BSDEs. |
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Keywords: | Backward stochastic differential equation Mean-field approach Mean-field BSDE Reflected BSDE Penalization method Viscosity solution |
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